Deeper than primes

[jsfisher]

Here a very simple model that explains OM's reasoning:

Your previous attempts have been abysmal failures, so do not expect us to have high expectations for this attempt. Nevertheless, proceed....

By OM's reasoning a line is the minimal form of Non-locality, where a point is the minimal form of Locality.

Well, you have confirmed our lack of high expectation was justified. Here's the annotated version:

By OM's [an undefined term] reasoning [what reasoning? Decree perhaps, but not reasoning] a line is the minimal form [in what sense minimal?] of Non-locality [another undefined term], where a point is the minimal form [in what sense minimal?] of Locality [yet another undefined term].

Now think about an infinitely long line that has two distinct points along it.

Ok, Captain Obvious, we can do that.

Since the line is infinitely long then no matter how far are the two points from each other they do not reach any edge because an infinitely long line is edgeless.

The points don't reach mauve, either. What's your point?

We call this case non-finite extrapolation.

No, we don't. You might, but that would be in line with you getting things so very, very wrong all the time.

The same thing works in the opposite direction.

No matter how close the points are they are still two distinct points.

Given that the two points were required to be distinct in the first place, this last statement of yours is stupid.

We call this case non-finite interpolation.

...but not as stupid as this statement. This statement is also wrong.

So by using this simple model we are able to understand both non-finite extrapolation and non-finite interpolation.

Why do you say this? The only thing clear from your statements is that you don't understand either extrapolation or interpolation.

Furthermore, by using, for example, finite extrapolation we are able to determine a fixed segment along the non-finite line, and only then concepts like closer or farer has a meaning with respect to the fixed segment.

Only by finite interpolation the two distinct points are able to become to a one point.

No.

Be aware of the fact that all these notions are achieved by using a model that is based on the linkage between Non-locality and Locality.

Actually, it is entirely based on your inability to understand simple mathematical concepts.

...<snip psychedelics>...

 

[dafydd]

Here a very simple model that explains OM's reasoning:

By OM's reasoning a line is the minimal form of Non-locality, where a point is the minimal form of Locality.

Now think about an infinitely long line that has two distinct points along it.

Since the line is infinitely long then no matter how far are the two points from each other they do not reach any edge because an infinitely long line is edgeless.

We call this case non-finite extrapolation.

The same thing works in the opposite direction.

No matter how close the points are they are still two distinct points.

We call this case non-finite interpolation.

So by using this simple model we are able to understand both non-finite extrapolation and non-finite interpolation.

Furthermore, by using, for example, finite extrapolation we are able to determine a fixed segment along the non-finite line, and only then concepts like closer or farer has a meaning with respect to the fixed segment.

Only by finite interpolation the two distinct points are able to become to a one point.

Be aware of the fact that all these notions are achieved by using a model that is based on the linkage between Non-locality and Locality.

Complex systems like us can use non-finite interpolation as a non-finite source of energy where the non-finite extrapolation is used as a non-finite environment for non-finite expression of complexity.

By this model we are actually living in a non-entropic universe, but since we get it only by using a finite point of view, we interpret it in terms of death by maximum entropy.

Furthermore we force our finite viewpoint on the non-finite interpolation or extrapolation and as a result we get the non-finite only in terms of Locality.

OM changes all this by providing a single model that enables to understand the linkage between Locality and Non-locality as they appear by infinite or finite interpolation or extrapolation.

One of the tools of this new paradigm is called a non-local number, which is used to deal with non-finite interpolation or extrapolation.

Hilarious,thank you.I needed a good laugh.

 

[leafman91]

Here a very simple model that explains OM's reasoning:

By OM's reasoning a line is the minimal form of Non-locality, where a point is the minimal form of Locality.

Now think about an infinitely long line that has two distinct points along it.

Since the line is infinitely long then no matter how far are the two points from each other they do not reach any edge because an infinitely long line is edgeless.

We call this case non-finite extrapolation.

The same thing works in the opposite direction.

No matter how close the points are they are still two distinct points.

We call this case non-finite interpolation.

So by using this simple model we are able to understand both non-finite extrapolation and non-finite interpolation.

Furthermore, by using, for example, finite extrapolation we are able to determine a fixed segment along the non-finite line, and only then concepts like closer or farer has a meaning with respect to the fixed segment.

Only by finite interpolation the two distinct points are able to become to a one point.

Be aware of the fact that all these notions are achieved by using a model that is based on the linkage between Non-locality and Locality.

Complex systems like us can use non-finite interpolation as a non-finite source of energy where the non-finite extrapolation is used as a non-finite environment for non-finite expression of complexity.

By this model we are actually living in a non-entropic universe, but since we get it only by using a finite point of view, we interpret it in terms of death by maximum entropy.

Furthermore we force our finite viewpoint on the non-finite interpolation or extrapolation and as a result we get the non-finite only in terms of Locality.

OM changes all this by providing a single model that enables to understand the linkage between Locality and Non-locality as they appear by infinite or finite interpolation or extrapolation.

One of the tools of this new paradigm is called a non-local number, which is used to deal with non-finite interpolation or extrapolation.

Cheers to whoever's picture that was, and apologies that I don't know who you are.

 

[Little 10 Toes]

Be aware of the fact that all these notions are achieved by using a model that is based on the linkage between Non-locality and Locality.

How can that be? There is no linkage at all since if we know the location of the line (locality), then we know the location of the points since you have said the points are on the line. If you claim that we don't know the where the points are on the line, but we know where the line is, then you have to make up a new term since you never answered my post. If we don't know where the line is, how do we know the location of the points? Won't that make everything non-local, or will you invent another term?

 

[dafydd]

How can that be? There is no linkage at all since if we know the location of the line (locality), then we know the location of the points since you have said the points are on the line. If you claim that we don't know the where the points are on the line, but we know where the line is, then you have to make up a new term since you never answered my post. If we don't know where the line is, how do we know the location of the points? Won't that make everything non-local, or will you invent another term?

Expect another invented term any time now.

 

[The Man]

<preceding nonsense snipped>

Complex systems like us can use non-finite interpolation as a non-finite source of energy where the non-finite extrapolation is used as a non-finite environment for non-finite expression of complexity.

<subsequent nonsense snipped>

Well now we have it, a practical use of OM as a “non-finite interpolation” “non-finite source of energy” “Complex systems like us can use”. I for one can hardly wait for the “non-finite interpolation” powered car, cell phone or perhaps just toaster. How about it Doron, can your “non-finite source of energy” from “non-finite interpolation” actually do anything, even simply toast bread or can it only feed your “non-finite” fantasies?

That was only 5 “non-finite”s in just one sentence. Come on Doron, I’m sure your can do better then that. Just tap into that “non-finite interpolation as a non-finite source of energy” and I’m sure you can come up with a “non-finite” statement based on the “non-finite expression” of “non-finite” complexity in a “non-finite environment” established by “non-finite interpolation” of “non-finite extrapolation” to demonstrate the “non-finite” power of your “non-finite” ignorance.

 

[doronshadmi]

The minimal form of total finite (Locality) is a point (a 0-dim element).

The minimal form of total non-finite (Non-locality) is an edgeless line (a 1-dim element).

A line segment is the minimal finite form, and it is the result of Non-locality\Locality linkage.


Given an arbitrary segment along the edgeless line, non-finite extrapolation between a pair of points is defined in terms of "farer w.r.t that line segment (there is no maxima because no segment can be an edgeless line.

Given an arbitrary segment along the edgeless line, non-finite interpolation between a pair of points is defined in terms of "closer w.r.t that line segment (there is no minima because no segment can be a single point.

Minima and maxima can be found only in the case of finite interpolation or extrapolation w.r.t that line segment.

 

[Little 10 Toes]

The minimal form of total finite (Locality) is a point (a 0-dim element).

The minimal form of total non-finite (Non-locality) is an edgeless line (a 1-dim element).

A line segment is the minimal finite form, and it is the result of Non-locality\Locality linkage.


Given an arbitrary segment along the edgeless line, non-finite extrapolation between a pair of points is defined in terms of "farer w.r.t that line segment (there is no maxima because no segment can be an edgeless line.

Given an arbitrary segment along the edgeless line, non-finite interpolation between a pair of points is defined in terms of "closer w.r.t that line segment (there is no minima because no segment can be a single point.

Minima and maxima can be found only in the case of finite interpolation or extrapolation w.r.t that line segment.

So now we are changing what local/non-local means? I specificly listed that local means known location and non-local means unknown location. A line segment, as well a line, are both 1-dimensional objects.

 

[zooterkin]

The minimal form of total non-finite (Non-locality) is an edgeless line (a 1-dim element).

What other sort of line is there? What do you mean by edgeless? What is a non-edgeless line? What do you mean by non-finite in this context? As a line is generally defined by the two endpoints, how is a line non-finite?

ETA: By 'non-finite', are you referring to the fact that there is an infinite number of points on a line? If so, it's not the line which is 'non-finite'; the line is very much finite, as it has ends.

 

[doronshadmi]

What other sort of line is there? What do you mean by edgeless? What is a non-edgeless line? What do you mean by non-finite in this context? As a line is generally defined by the two endpoints, how is a line non-finite?

ETA: By 'non-finite', are you referring to the fact that there is an infinite number of points on a line? If so, it's not the line which is 'non-finite'; the line is very much finite, as it has ends.

An edgeless line is a line that has no beginning AND no end.

This element exits even if there is no single point along it.

The same holds about a point. It exists even if there is no line at all.

 

[Little 10 Toes]

An edgeless line is a line that has no beginning AND no end.

This element exits even if there is no single point along it.

The same holds about a point. It exists even if there is no line al all.

A line, by definition, has no end. Why even use extra words?

Edit:
From wikipedia: In Euclidean geometry, a line is a straight curve. When geometry is used to model the real world, lines are used to represent straight objects with negligible width and height. Lines are an idealisation of such objects and have no width or height at all and are usually considered to be infinitely long.

 

[doronshadmi]

So now we are changing what local/non-local means? I specificly listed that local means known location and non-local means unknown location. A line segment, as well a line, are both 1-dimensional objects.

Only an 0-dim element has a known location.

This is not true for both an edgeless line or a line segment, which are 1-dim elements.

How can that be? There is no linkage at all since if we know the location of the line (locality), then we know the location of the points

You know the accurate location of the points, but not the accurate location of the line between them, exactly because logically the line segment is on AND not-on the location w.r.t each one of the points (it is non-local w.r.t each one of them).

On the contrary, each point is on XOR not-on w.r.t the line segment (each point is local w.r.t the line segment).

 

[Little 10 Toes]

Only an 0-dim element has a known location.

This is not true for both an edgeless line or a line segment, which are 1-dim elements.

So you finally respond to me after I post 4-6 times. How about going back and answering this post here?

 

[Little 10 Toes]

Only an 0-dim element has a known location.

This is not true for both an edgeless line or a line segment, which are 1-dim elements.

But what about the end points of a line segment? Are they 0-dimensional or not? If they are, then since the points locations are know, we know the location of the line segment. If they are not 0-dimesional, then the line segment is not a line segment.

From wikipedia:
In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square.

 

[doronshadmi]

Furthermore, by using, for example, finite extrapolation we are able to determine a fixed segment along the non-finite line, and only then concepts like closer or farer has a meaning with respect to the fixed segment.

No.

You are right about that part, it is wrong.

I fixed it in http://www.internationalskeptics.com/forums/showpost.php?p=5235905&postcount=6267.

But here it is again with a better version:

The minimal form of total finite (Locality) is a point (a 0-dim element).

The minimal form of total non-finite (Non-locality) is an edgeless line (a 1-dim element).

A line segment is the minimal non-total finite form, and it is the result of Non-locality\Locality linkage.

Given an arbitrary segment along the edgeless line, non-finite extrapolation between a pair of points is defined in terms of "farer w.r.t that line segment (there is no maxima because no segment can be an edgeless line).

Given an arbitrary segment along the edgeless line, non-finite interpolation between a pair of points is defined in terms of "closer w.r.t that line segment (there is no minima because no segment can be a single point).

Minima and maxima can be found only in the case of finite interpolation or extrapolation w.r.t that line segment.

The difference between finite\infinite interpolation\extrapolation is clearly shown by the 0.999… example in post http://www.internationalskeptics.com/forums/showpost.php?p=5223529&postcount=6164.

 

[doronshadmi]

But what about the end points of a line segment? Are they 0-dimensional or not? If they are, then since the points locations are know, we know the location of the line segment. If they are not 0-dimesional, then the line segment is not a line segment.

From wikipedia:
In geometry, a line segment is a part of a line that is bounded by two end points, and contains every point on the line between its end points. Examples of line segments include the sides of a triangle or square.

Please look at the second part of http://www.internationalskeptics.com/forums/showpost.php?p=5236644&postcount=6272.

 

[doronshadmi]

I for one can hardly wait for the “non-finite interpolation” powered car, cell phone or perhaps just toaster.

They made fun of irrational numbers.

They made fun of negative numbers.

They made fun of imaginary numbers.

Now they are making fun of non-local numbers and tomorrow the will make fum of another kind of numbers.

The Man you belong to a community persons that making fun and fail, all along our short history.

You are defiantly not the first and probably not the last member of this community.

( Also you ignored the last part of http://www.internationalskeptics.com/forums/showpost.php?p=5232214&postcount=6244 and the middle part of http://www.internationalskeptics.com/forums/showpost.php?p=5232288&postcount=6249 ).

 

[The Man]

Only an 0-dim element has a known location.

This is not true for both an edgeless line or a line segment, which are 1-dim elements.

Fine, under OM one can not “know” the location of a line or line segment. That puts your OM at a severe disadvantage when compared to geometry.

You know the accurate location of the points, but not the accurate location of the line between them,

Again simply a contradiction, the “accurate location of the line” is “the accurate location of the points” including those other points “between them”. Since under OM you can not know the location of a line segment then you also can not know the location of the points that define the line segment.

exactly because logically the line segment is on AND not-on the location w.r.t each one of the points (it is non-local w.r.t each one of them).

Logically that is also simply a contradiction, as you claim the proposition that the “line segment is on” and its negation “not-on” are both true for the same point.

On the contrary, each point is on XOR not-on w.r.t the line segment (each point is local w.r.t the line segment).

Each point between the end points of the line segment is “on” the line segment (more specifically included in a set representing the line segment) no “XOR”s about it.

Been albe to find your “unknown” gaps in a set representing a line segment yet Doron?

Got a design for a “non-finite interpolation” powered toaster yet Doron?

Got anything from your OM, Doron, other then you claiming that you can not even do just basic geometry with it since you can not known the location of a line segment?

 

[The Man]

They made fun of irrational numbers.

They made fun of negative numbers.

They made fun of imaginary numbers.

Now they are making fun of non-local numbers and tomorrow the will make fum of another kind of numbers.

The Man you belong to a community persons that making fun and fail, all along our short history.

You are defiantly not the first and probably not the last member of this community.

So design a “non-finite interpolation” powered toasted or show any use for your “non-local numbers” other then just you claiming you can’t locate them. So far all you can show is that you play hide and seek with your “non-local numbers” so having fun with them is currently their only demonstrated use.

( Also you ignored the last part of http://www.internationalskeptics.com/forums/showpost.php?p=5232214&postcount=6244 and the middle part of http://www.internationalskeptics.com/forums/showpost.php?p=5232288&postcount=6249 ).

You have been informed numerous times that I simply will not condone your childish behavior of surreptitiously editing posts.

 

[Little 10 Toes]

So now we are changing what local/non-local means? I specificly listed that local means known location and non-local means unknown location. A line segment, as well a line, are both 1-dimensional objects.

Only an 0-dim element has a known location.

This is not true for both an edgeless line or a line segment, which are 1-dim elements.

How can that be? There is no linkage at all since if we know the location of the line (locality), then we know the location of the points since you have said the points are on the line. If you claim that we don't know the where the points are on the line, but we know where the line is, then you have to make up a new term since you never answered my post. If we don't know where the line is, how do we know the location of the points? Won't that make everything non-local, or will you invent another term?

You know the accurate location of the points, but not the accurate location of the line between them, exactly because logically the line segment is on AND not-on the location w.r.t each one of the points (it is non-local w.r.t each one of them).

On the contrary, each point is on XOR not-on w.r.t the line segment (each point is local w.r.t the line segment).

First of all this post has been reported because you did not take the time to post a new message after I have posted two.

Second, a line segment includes the two end points. You have already said we know the location of 0-dimensional elements a.k.a. points. We now know were the line segment starts and stops due to the end points. The line segment includes all the points between the endpoints. Since points are 0-dimensional, we know where all their locations are.

Third, why do we know the "accurate location"? Are you saying that we only knew the approximate location before?

Fourth, you still haven't explained how a line segment is on or not on the point. To my understanding, XOR means either/or, but not both. Please explain why a point on the line segment (which includes ALL points between the end points) is not part of the line segment.