Deeper than primes

[drkitten]

In general Relation cannot be but Non-local, where an Element can be Non-local of Local w.r.t another Element.

If I wrote that an Element cannot be but local, then I was wrong.

You weren't even wrong. You weren't even meaningful.

 

[ddt]

Because that change is so important in interpreting the otherwise meaningless gibberish.

In approximately the same way that a turd sandwich is much better when made with dijon mustard instead of the ordinary yellow stuff.

Is this the right place to point out there is a significant difference between dijon mustard and ketchup? For those who want to keep track of time as well want to savour now and then some mustard, the integrated solution of a mustard watch is feasible; whereas for ketchup, you'd need at least a teaspoonful for a good tasting, which is beyond the limitations of a wrist watch.

Lit.: Yann-Joachim Ringard, "Mustard Watches: an integrated approach to time and food".

I suggest a much simpler rewriting of the relevant post:

It has to be:

"[Every word that Doron writes] cannot be understood and be developed [and should be] totally ignored."

That's worth being repeated, for the hapless who might bump into this thread unprepared.

BTW, notice what happened to the "Consciousness" thread?

 

[jsfisher]

BTW, notice what happened to the "Consciousness" thread?

More importantly, notice what happened to our main lecturer. He has apparently taken a one week sabbatical.

 

[ddt]

More importantly, notice what happened to our main lecturer. He has apparently taken a one week sabbatical.

Apparently, he had run out of straws to grasp at.

 

[Apathia]

Darn! I totally missed that the circus had moved there.

 

[drkitten]

Is this the right place to point out there is a significant difference between dijon mustard and ketchup? For those who want to keep track of time as well want to savour now and then some mustard, the integrated solution of a mustard watch is feasible; whereas for ketchup, you'd need at least a teaspoonful for a good tasting, which is beyond the limitations of a wrist watch.

Lit.: Yann-Joachim Ringard, "Mustard Watches: an integrated approach to time and food".

That is brilliant. The truly scary thing is that Dr. Ringard's mathematics is substantially better -- more rigorous, more creative, and above all, more coherent -- than Doron's.

 

[ddt]

That is brilliant. The truly scary thing is that Dr. Ringard's mathematics is substantially better -- more rigorous, more creative, and above all, more coherent -- than Doron's.

But then, Dr. Ringard is known for "System F" and "Linear Logic". He knows his stuff. And maybe indeed, an occasional lick of mustard gives inspiration.

 

[doronshadmi]

A part of the first post:

The non-local ur-element is the maximum entropy of itself (no differences can be found within it). Also a local ur-element is the maximum entropy of itself (no differences can be found within it).

Maximum entropy exists in both non-locality and locality, but they are opposite by their self nature, so if non-locality and locality are associated, then a non-entropic domain is created.

I improved http://www.geocities.com/complementarytheory/UR.pdf.

By carefully reading all of it, one can understand post 1 ( http://www.internationalskeptics.com/forums/showpost.php?p=4083359&postcount=1 ).

 

[ddt]

I improved http://www.geocities.com/complementarytheory/UR.pdf.

I bet improving means that you put even more gibberish and nonsense in it? I, at least, won't bother downloading it. You don't even bother to indicat what you might have changed, and I doubt you even know what you changed.

By carefully reading all of it, one can understand post 1 ( http://www.internationalskeptics.com/forums/showpost.php?p=4083359&postcount=1 ).

That's not the way it works here. You could simply have improved post #1. But at post #688, you have not been able to explain the various questions about post #1, so why could you do that in a PDF we should download?

 

[jsfisher]

I bet improving means that you put even more gibberish and nonsense in it? I, at least, won't bother downloading it. You don't even bother to indicat what you might have changed, and I doubt you even know what you changed.

Ok, but then you will miss such gems as:

Definition 4: An object that is distinguished from another object by exactly one relation, is called Local.

Example: a point is a local object.

So, "Local" is a relative concept. An object is local with respect to another object. But why then does doron cite "a point" as an example of a local object without providing its relative referent?

Also, how hard is it to establish more than one relation between any two distinct objects?

In other words, nothing is local. Doron has provided a non-standard definition for the empty set.

 

[doronshadmi]

Ok, but then you will miss such gems as:




So, "Local" is a relative concept. An object is local with respect to another object. But why then does doron cite "a point" as an example of a local object without providing its relative referent?

Also, how hard is it to establish more than one relation between any two distinct objects?

In other words, nothing is local. Doron has provided a non-standard definition for the empty set.

No,

A relation cannot be but non-local w.r.t any given element.

A line segment can be local or non-local w.r.t another element.

A point cannot be but local w.r.t another element.

Please read all of http://www.geocities.com/complementarytheory/UR.pdf very carefully, then think about it before you reply.

You will not get it by using only a step-by-step observation, as explained in pages 6-7.

I did not provide a non-standard defitition of the empty set.

I provide the pre-axiomatic terms that enables this axiom, in the first place.

 

[jsfisher]

A point cannot be but local w.r.t another element.

Nonsense.

Consider a point and any line which does not include that point. I'll use the line as my point of reference.

Relation 1: The point is not on the line.
Relation 2: The point is not equal to the line.
Relation 3: The point and line share a common plane.

Shall I go on?

Three relations between point and another element, namely the line. According to your definition, the point is non-local with respect to the line.

Please read all of http://www.geocities.com/complementarytheory/UR.pdf very carefully, then think about it before you reply.

You will not get it by using only a step-by-step observation, as explained in pages 6-7.

I put far more care into reading it than you put into writing it.

 

[Apathia]

Apathia the Mad Gardener cannot resist.

From the UR.pdf:

A non-local element (which is not defined by (not made of) any collection of local
elements) can be both a member and not a member of any given non-empty set.
Therefore, non-locality is a property that is stronger than any cardinal of any non-empty
set of local members. As a result, any non-empty set of local members, is incomplete by
definition.

Lets say we represent the Local/Non-Local Complementation by a table with some fruit on it.
The bare tabletop represents Non-Locality. Distinguising individual items of fruit represents Locality. A bowl of oranges represents the complementation of Relation and Element. The oranges are elements. A relation of classification identifies, lets say three, of them as members of the bowl of oranges.
How many oranges are there?
Three it seems.
But suppose there are some other oranges on the table that have not been localized in the bowl. They are non-local to it. They haven't been counted among the elect.
How many oranges are there? Well, I don't know how many are rolling around on the table. Are these virtual oranges?
I can say how many are in the bowl, can't I? A total of three in the bowl.
It would seem that my bowling relation both includes and excludes.
So the total, complete number of oranges in the bowl is three.

However:
Doron, it seems by your reckoning those non-local oranges that by non-locality are everywhere and nowhere are and are not in the bowl.

So, the one hundred and forty-four thousand dollar question:
Are there more than three oranges in the bowl?

Remember:

non-locality is a property that is stronger than any cardinal of any non-empty
set of local members.

 

[doronshadmi]

Relation 1: The point is not on the line.
Relation 2: The point is not equal to the line.
Relation 3: The point and line share a common plane.

Observations 1 and 2 are the result of observation 3 (where the plane is the non-local w.r.t a point or a line).

Furthermore, there is an OR condition between observation 1 and observation 2, where non-locality is an AND condition between two relations of the same observer.

You have to learn how things are observed by x. If two different relations are gathered by an AND condition in the same x, then x is non-local.


You used the non-locality of a plane w.r.t a point or a line, in order to conclude something about a point.

y (which is a point or a line) is observed through x (a plane).

x (a plane) is non-local w.r.t y (which is a point or a line) if:

x < = y

x > = y

x < > y


x = point

In all cases the same point (nontated as x) cannot be in more than a one relation with any given y.

You still do not get that "y observed through x" is non-commutative, where x is the observer and y is the observed.

 

[jsfisher]

Observations 1 and 2 are the result of observation 3 (where the plane is the non-local w.r.t a point or a line).

They are relations. If anything, relation #3 is a consequence of #1, not the other way around. But you can learn geometry on your own. Right now, the topic is your definition #4.

Your definition #4 is bogus. It doesn't do what you think it does.

As stated, object #1 is "local" with respect to object #2 if and only if there exists exactly one relation between the two.

Between any point and any line, there exist more than one relation. Whether the relations are "related" is of no consequence; that's not an aspect of your definition. By your definition, a point is not local with respect to a line.

If that is not what you meant (and seldom is what you write what you mean), then you need a new definition.

 

[doronshadmi]

Apathia the Mad Gardener cannot resist.

From the UR.pdf:



Lets say we represent the Local/Non-Local Complementation by a table with some fruit on it.
The bare tabletop represents Non-Locality. Distinguising individual items of fruit represents Locality. A bowl of oranges represents the complementation of Relation and Element. The oranges are elements. A relation of classification identifies, lets say three, of them as members of the bowl of oranges.
How many oranges are there?
Three it seems.
But suppose there are some other oranges on the table that have not been localized in the bowl. They are non-local to it. They haven't been counted among the elect.
How many oranges are there? Well, I don't know how many are rolling around on the table. Are these virtual oranges?
I can say how many are in the bowl, can't I? A total of three in the bowl.
It would seem that my bowling relation both includes and excludes.
So the total, complete number of oranges in the bowl is three.

However:
Doron, it seems by your reckoning those non-local oranges that by non-locality are everywhere and nowhere are and are not in the bowl.

So, the one hundred and forty-four thousand dollar question:
Are there more than three oranges in the bowl?

Remember:

Orenge in the bowl or on the table = *

The bowl = [*,*,*]

* is local w.t.r the bowl.

The bowl is non-local w.r.t any *.

The table (notated by "{" and "}") is non-local w.r.t the bowl ( notated as{[]} ) or to any given * no matter if it is in the bowl or not.

{[*,*,*,*,[*,*,*]*,*,...} or in other words, any given orange is local w.r.t the table, the bowl, or to any * .

 

[Apathia]

Orenge in the bowl or on the table = *

The bowl = [*,*,*]

* is local w.t.r the bowl.

The bowl is non-local w.r.t any *.

The table (notated by "{" and "}") is non-local w.r.t the bowl ( notated as{[]} ) or to any given * no matter if it is in the bowl or not.

{[*,*,*,*,[*,*,*]*,*,...} or in other words, any given orange is local w.r.t the table, the bowl, or to any * .

Thanks for restatement.
But please imagine I'm a grade schooler, first grade.
The lesson is using Organic Natural Numbers.
I come up to the table and count three oranges in the bowl.
I say there are no more than three oranges in the bowl.
Explain to me how I have failed in my accounting. Or, if I'm right, if what way ONNs agknowledge the oranges outside the bowl, but maintain a definite number within the bowl.
How do ONNs address the question of how many?

Please imagine I'm a small child. (I'm not really that far from being one according to my ex-girlfriend.)

 

[ddt]

Ok, but then you will miss such gems as:

Definition 4: An object that is distinguished from another object by exactly one relation, is called Local.

Example: a point is a local object.

So, "Local" is a relative concept. An object is local with respect to another object. But why then does doron cite "a point" as an example of a local object without providing its relative referent?

Also, how hard is it to establish more than one relation between any two distinct objects?

In other words, nothing is local. Doron has provided a non-standard definition for the empty set.

Very good observation, jsfisher! I see my prediction

and I doubt you even know what you changed.

was quite spot-on.

I see doron tries to deny your conclusion and your example. It's clear he simply doesn't get the point of your argument. I'll try another approach. It's even constructivist, i.e., I won't be using argument by contradiction .

Let's first see what it should mean that "an object x is distinguished from another object y by relation R". IMNSHO, this can only mean that there is a third object z such that

(x, z) in R and not (y, z) in R or not (x, z) in R and (y, z) in R​

in other words: the question "with which objects is z related by R" is answered differently for x and y.

Let's take two different points A and B. Then draw the circle with centre A and radius the length of the line segment AB. Likewise, draw the circle with centre B and the same radius. These two circles have two intersection points; call them C and D.

With four (known) points, we can make 2^16 different relations between these points. I just define two different ones now:

R1 := { (A, C) }
R2 := { (B, C) }​

Now it's clear that R1 distinguishes A from B, as (A, C) is in R1 and (B, C) is not. Likewise, R2 distinguishes A from B.

As we have now two relations that distinguish A from B (and I could define many more), A is not local. QED.

Yes, it's clear this definition of "local" is nonsensical. It's also again clear that doron doesn't understand the basest and simplest mathematical arguments.

 

[Skeptic]

Doron --

I don't know how to tell you this, but why don't you go and take first-year mathematics at the Open University? Then, you might have some idea why what you're talking about is nonsense.

Just think of all you could have achieve with the time and effort you put into this absolutely futile and meaningless "theory" (actually, meaningless gibberish) of yours. Sigh.

 

[doronshadmi]

Between any point and any line, there exist more than one relation.

There is an OR connective between any pair of relatrions between a point and a line, for example:

x = .
y = __

x is local w.r.t y if:

x < y (example: . __ )

or

x = y (example: ( _. , _._ , ._ )

or

x > y (example: __ . )



This is not the case if:

x = __
y = .

x is local w.r.t y if:

x < y (example: __ . )

or

x > y (example: . __ )


x is non-local w.r.t y if:

x < and = y (example: _. )

x < and > y (example: _._ )

x = and > y (example: ._ )

Pay attantion that no plane was used here, but only a single point and a single line segment.