Deeper than primes

[Richard Masters]

Why doronshadmi? Why TMiguel?

 

[ddt]

In this case, any observation is only from x, and any conclusion is only about x.

Please look also at http://www.internationalskeptics.com/forums/showpost.php?p=4221149&postcount=734 .

What do you mean with observation and conclusion? Are you deliberately being obtuse?

Your symbol = denotes a relation. A relation is a set of pairs. So do you mean that your symbol = denotes the relation { (x, x) }, and your symbol ≠ denotes the relation { (x, y) | y is unequal to x }?

So how do I know which x your = refers to? Your notation doesn't make this clear, which could be done, e.g., by subscripting with x: =_x, as the relations =_x and =_y, for different x and y, are two different relations.

In X = Y, either they are the same or they are not. The equal relation is symmetric. X = Y implies Y = X. Nothing "is observed through" anything else.

If you need such a concept, then you need to express it in your definitions. You also need to pick some new symbols; the equal sign has a well-established meaning already.

Yes, the = symbol denotes an equality relation, which at least satisfies the laws of an equivalence relation.

As usual, doron, you display your utter ignorance of mathematics.

 

[Apathia]

What I say is this:

Any researchable thing cannot be complete (total).

By my notion, a set is the result of an interaction between two totalities, which are Isolation and Connectivity.

Objects are a non-total version of Isolation where Relations are a non-total version of Connectivity where a set is the result of Relation\Object Interaction, and therefore non-total (or incomplete).

EDIT:

One of my aims is to show that in addition to, so called, objective and external point of view w.r.t researched mathematical subjects, there can be many other points of view that may change our understanding of these subjects.

In other words, the observer's point of view must not be ignored and by using it we can improve (by training) our abilities to use observation in more fruitful ways.

So what I count as three oranges in the bowl, another can count as four?
And the squarer root of 144 can be lots of different numbers?
And quantity is all relative?

What you are tragically missing is the precision of Mathmatics to yield definite quantities according to defined relations.
To get to the relativity you want, you have destroyed definition.
And you have destoyed it for the obeserver as well. Since she can say three anytime she pleases, her statement of quantity looses any value.

Your complementary approach doesn't necessarily lead to this slime.

One of my aims is to show that in addition to, so called, objective and external point of view w.r.t researched mathematical subjects, there can be many other points of view that may change our understanding of these subjects.

I get your philosophical intent. I'm glad you said "in addition to." Because if you chuck out objective quantity and defined relation, you kill your intent as well. With no defined point of view from which to speak, you indeed have nothing but gibberish.

Take The Special Theory of Relativity for example. It asserts the relativity of observers in respect to duration and extension. But its precise Mathmatical expression gives us the ability to calculate just how much time will be slowed or space will be contracted. Its not a free for all where there is no definition and observers can't coherently relate their observations.

Some of us have suspected you have a cognitive difficulty manipulating embedded classes.
New ideas involve new ways data is related in classes. It's all about new deffinitions of association. We deal with exclusion by a wider inclusion. I am Human. Human includes Asian. But I'm not Asian. I am excluded from that classifier.
But potential racial predjudice isn't overcome by declaring that the set of Asian includes Caucasion as well. Its in the wider classifier of Human.

If you want to slip into a state of non-local consciouness, go ahead. But when you get back to the researchable, cognitive, world, you are going to be manipulatng defined boundaries.

That's what Mathematics is all about: defined boundaries.

I really hope you aren't chucking them and calling it a new paradigm.
Because without objective, defined relation, boundaries that hold their exclusive contents, you have nothing.

And don't try to invoke something like "quantum tunneling" here.
We have a Mathematics of Quantum Theory that deals wth those events in objective precision.

You can have your observers with different points of view. But when they talk to each other, they better have a common language with words whose meanings are more than subjective.
Or you're just going to have a Babel.

Now you still haven answerd my question about ONNs and countable quantity. What is quanity in rerspect to ONNs?
And does it mean that the quanity of oranges in the bowl cannot be determined?

 

[doronshadmi]

In X = Y, either they are the same or they are not. The equal relation is symmetric. X = Y implies Y = X. Nothing "is observed through" anything else.

If you need such a concept, then you need to express it in your definitions. You also need to pick some new symbols; the equal sign has a well-established meaning already.

Dear jsfisher,

Your determinations , and so my determinations are based on point of view of the researched mathematical subjects.

For example: Y=X = X=Y is a symmetric point of view of X,Y relation, where my point of view is asymmetric.

By using an asymmetric point on view, the difference between non-locality and locality can be defined.

By using a symmetric point of view the difference between non-locality and locality cannot be defined.

So the general idea of my work is not to get mathematical subjects from any exclusive point of view, because additional points of view of the researched mathematical subjects, may lead us to define more interesting results about, so called, already agreed definitions.

 

[doronshadmi]

That's what Mathematics is all about: defined boundaries.

For me Mathemathics is to define relations between boundaries by not using any exclusive obseraviton.

Relations are non-local, element are local or non-local and non-exclusive obseraviton is used in order to interact and understand them.

 

[jsfisher]

By using an asymmetric point on view, the difference between non-locality and locality can be defined.

No, all you are doing is using well-defined symbols and constructs to mean undefined things.

Your Definition #4, in any of its revisions, remains a complete failure.

Here's a tip: If something isn't symmetric, don't define it as symmetric.

 

[Apathia]

What I say is this:

Any researchable thing cannot be complete (total).

Yep.
But here's the qualifier that Mathmatics depends upon:
It can be relatively complete according to a specified relation.
We manipulate classifiers of relation all the time, understanding that inclusion and exclusion are realtive to a defined relaltion of commonality.

We get stuck behind boundaries, not because there are boundaries but because we accept no relations that transcend them.
But transcendance doesn't erase boundaries or turn them into mushy mud. It enables new cnfigurations.
I can put another orange in that bowl.
I can make a bowl of fruit that contains oranges ands bannanas.
I can talk about all the fruit in all the bowls on the table.
All thanks to Locality and Non-Locality.

The playing field does not mix up the teams.

 

[doronshadmi]

No, all you are doing is using well-defined symbols and constructs to mean undefined things.

Your Definition #4, in any of its revisions, remains a complete failure.

Here's a tip: If something isn't symmetric, don't define it as symmetric.

Please show the symmetry in definition #4:

Definition 4: If object x = or ≠ (where ≠ is < or >) w.r.t object y, then object x is called Local.

Also please show the symmetry in definition #5:

Definition 5: If object x = and ≠ (where ≠ is < or >) or < and > w.r.t object y, then object x is called Non-Local.


Hint: Do not force Y=X = X=Y on them.

As for symbols, their meaning can be changed by using non-exclusive observations.

 

[doronshadmi]

Yep.
But here's the qualifier that Mathmatics depends upon:
It can be relatively complete according to a specified relation.
We manipulate classifiers of relation all the time, understanding that inclusion and exclusion are realtive to a defined relaltion of commonality.

We get stuck behind boundaries, not because there are boundaries but because we accept no relations that transcend them.
But transcendance doesn't erase boundaries or turn them into mushy mud. It enables new cnfigurations.
I can put another orange in that bowl.
I can make a bowl of fruit that contains oranges ands bannanas.
I can talk about all the fruit in all the bowls on the table.
All thanks to Locality and Non-Locality.

The playing field does not mix up the teams.

http://www.internationalskeptics.com/forums/showpost.php?p=4221408&postcount=745

 

[Apathia]

For me Mathemathics is to define relations between boundaries by not using any exclusive obseraviton.

Relations are non-local, element are local or non-local and non-exclusive obseraviton is used in order to interact and understand them.

Now you still haven answerd my question about ONNs and countable quantity. What is quanity in rerspect to ONNs?
And does it mean that the quanity of oranges in the bowl cannot be determined?

 

[jsfisher]

Please show the symmetry in definition #4:

Definition 4: If object x = or ≠ (where ≠ is < or >) w.r.t object y, then object x is called Local.

In your .PDF you explicitly define your notation thus: "= relation is equal to...≠ relation is not equal to..." In this very thread you restricted "equal" to just logical identity and cited a wikipedia article.

With or without that added qualifier, your use of = and ≠ are of symmetric relations.

...and that "w.r.t." doesn't mean what you think it means in that definition. It still makes it into gibberish.

 

[ddt]

Definition 4: If object x = or ≠ (where ≠ is < or >) w.r.t object y, then object x is called Local.

A definition that doesn't make sense - apart from the superfluous word "object" and the idiotic juggling with relation symbols, so let's first simplify that part:

If x = y, then x is called local.​

What does this mean? Does it (a) mean:

If there is an y such that x = y, then x is called local.​

which would be nonsense, as trivially, substituting x for y makes that every x is called local.

Or does it (b) mean:

If for all y, x = y holds, then x is called local.​

which would be nonsense too as there surely will be at least one y for which x =y does not hold.

Or does it (c) mean:

If x = y, then x is called local to y​

an addition that does make sense, but which you've emphatically denied previously.

In terms of logic propositions: you have an unbound variable in your definition.

You made a definition with a hole you can drive a truck through. Anyone with half a brain can spot that.

Definition 5: If object x = and ≠ (where ≠ is < or >) or < and > w.r.t object y, then object x is called Non-Local.

Ditto.

 

[The Man]

Please show the symmetry in definition #4:

Definition 4: If object x = or ≠ (where ≠ is < or >) w.r.t object y, then object x is called Local.

Also please show the symmetry in definition #5:

Definition 5: If object x = and ≠ (where ≠ is < or >) or < and > w.r.t object y, then object x is called Non-Local.

Hint: Do not force Y=X = X=Y on them.

Uhm you do remember this post don’t you

I have to add that I use "=" as self identity ( http://en.wikipedia.org/wiki/Identity_(philosophy) )

That is what self identity means (from your link).

Logic of identity
In logic, the identity relation is normally defined as the relation that holds only between a thing and itself. That is, identity is the two-place predicate, "=", such that for all x and y, "x = y" is true iff x is the same thing as y. Identity is transitive, symmetric, and reflexive. It is an axiom of most normal modal logics that for all x, if x = x then necessarily x = x. (These definitions are of course inapplicable in some areas of quantified logic, such as fuzzy logic and fuzzy set theory, and with respect to vague objects.)

Self identity or sameness infers Y = X (or Y same as X) is the same as X = Y (or X same as Y). No one is forcing “Y=X = X=Y” you have simply volunteered that association since you claim to “use "=" as self identity”. So your “x = or…” use in definition 4 confers the symmetry of self identity.

As for symbols, their meaning can be changed by using non-exclusive observations.

So, since you are using exclusive observations (claiming X w.r.t. Y is different or exclusive of Y w.r.t. X) indicates that you are not changing the meaning of ‘"=" as self identity’, when considering Y = X and thus X w.r.t. Y is the same as Y w.r.t. X in that consideration. Either you have abandoned that notion of Y w.r.t. X being different from X w.r.t. Y (when considering X = Y) or you do not “use "=" as self identity”, make up your mind then get back to us.

 

[doronshadmi]

In your .PDF you explicitly define your notation thus: "= relation is equal to...≠ relation is not equal to..." In this very thread you restricted "equal" to just logical identity and cited a wikipedia article.

With or without that added qualifier, your use of = and ≠ are of symmetric relations.

...and that "w.r.t." doesn't mean what you think it means in that definition. It still makes it into gibberish.

The asymmetry is that X is compared to Y but Y is not compared to X.

This is the meaning of y is obsereved through x, but not vice versa.

By using this asymmetry a non-local object is distingushed from a local object.

In the case of = or ≠ , both are non-local, because any relation cannot be but non-local.

You mix between relations and objects, which is gibberish from my point of view.

EDIT:

Again:

x = .

y= ___

x = y from x point of view (for example: .__ , _._ , __. )

But y < and = x from y point of view (for example: __. )

or

y < and > x from y point of view (for example: _._ )

or

y > = and x from y point of view (for example: .__ )


So where is your x=y = y=x symmetry?

 

[jsfisher]

The asymmetry is that X is compared to Y but Y is not compared to X.

That's not what you wrote, and that's not what "compare" means.

 

[The Man]

The asymmetry is that X is compared to Y but Y is not compared to X.

This is the meaning of y is obsereved through x, but not vice versa.

By using this asymmetry a non-local object is distingushed from a local object.

In the case of = or ≠ , both are non-local, because any relation cannot be but non-local.

You mix between relations and objects, which is gibberish from my point of view.

While you just make things up then apply them inconsistently (or asymmetrically as you now seem to prefer to call it) even by your own professed definitions, which results in gibberish, from anyone’s point of view.

 

[doronshadmi]

That's not what you wrote, and that's not what "compare" means.

You are right, your "compare" is symmetric, my "compare is not.

And no point of view is exclusive.

 

[doronshadmi]

While you just make things up then apply them inconsistently (or asymmetrically as you now seem to prefer to call it) even by your own professed definitions, which results in gibberish, from anyone’s point of view.

Magority does not meas exclusive.

Please read the EDIT: (<--- I have learned something from you) in http://www.internationalskeptics.com/forums/showpost.php?p=4221692&postcount=754 .


EDIT: Any mathematical subject can be changed by using non-exclusive observations.

 

[doronshadmi]

Why? If considering a circle taken from some X Y origin and defined by X² + Y² = R². Any Radius R_Xn,Yn that is not equal to R_X1,Y1 would be defined as all radii both greater to and less then R_X1,Y1 or R_Xn,Yn ≠R_X1,Y1 is the same as R_Xn,Yn < and > R_X1,Y1.

So you used the asymmetric case of:

x = _____

y = __

x < and > w.r.t y (for example: ______)

I wish to see you doing it when:

x = .

y = ___

 

[jsfisher]

You are right, your "compare" is symmetric, my "compare is not.

And no point of view is exclusive.

First, the word being used is "equal to", not "compare". You even provided a reference for your usage, and the reference is clear. "Equal to" is a symmetric relation.

Second, if you goal is to be obtuse and confuse the discussion, you are doing an excellent job. Continue to abuse common usage and hide behind secret meanings. Well done!

I was looking for communication. My bad.