A hidden assumption

[doronshadmi]

Another pile of drivel.

Another example of ignorence.

 

[doronshadmi]

As clever and as devastating as Zeno of Elea.

No researchable thing is complete (is total).

We are very lucky that this is the case, because there is no limit to any development at the non-arbitrary game of evolution.

 

[jsfisher]

Still waiting for your evidence that a line is not defined as a collection by Standard Math (and you have to do it without using a function, because a function is non-local, otherwise no two things can be related with each other without its non-locality).

I didn't make the claim. You did, so the obligation falls to you to support your statement.

But you can't, can you? So it is with just about all of your claims. You cannot support them. Instead, you wave your hands and stamp your feet, then accuse us of being the problem.

You think and act like a 5 year-old, and chastise us for not doing the same. Did you know that 5 year-olds cannot grasp the concept of number? Sure, they can cope with 3 oranges or 3 pencils, but not with just 3. That's too abstract. Then again, that's where evolution (which you cherish but understand not) has brought us: Cognitive abilities develop in children as they mature; there is no "inherited knowledge", quite the opposite, in fact.

Many 5 year-olds have imaginary friends, too. doronshadmi, do you have imaginary friends?

 

[sol invictus]

PixMisa will say that anything that is undefined is meaningless.

Do you agree with him?

I'd prefer to let her/him speak for her/himself (English really has a major deficiency).

Language enables communication, and in order to communicate, one must share a common vocabulary. You insist on using standard terms in non-standard ways, and at the same time you refuse to give definitions of your usage.

If you talk to someone using language they cannot understand, you're the fool.

 

[jsfisher]

PixMisa will say that anything that is undefined is meaningless.

Do you agree with him?

You missed the whole point. Hilbert was saying (correctly) that what points, lines, and planes are is inferred from the axioms. Geometry, after all, is an axiomatic system (and not subject to Gödel's incompleteness theorems, by the way).

Euclid did offer definitions for points and lines, but in and of themselves they are not all that helpful. It is from the axioms of geometry that the definitions take on substance.

 

[Apathia]

No researchable thing is complete (is total).

We are very lucky that this is the case, because there is no limit to any development at the non-arbitrary game of evolution.

And we are lucky that mathematics is able to transcend the restrictions you slap on it.

 

[doronshadmi]

Did you know that 5 year-olds cannot grasp the concept of number?

By standard mathematics you have Natural Numbers, Rational Numbers, Irrational numbers, etc... , but there is no general definition to Number.

Children may not understand the sophisticated manipulations that adults can do with numbers, but they have a simple (and simple is not trivial) point of view of the concepts that can lead to the general definition of Number, as I did in my theory.

A number is the simplest building-block of the researchable.

Your sophisticated manipulations of that building-block, do not allow you to get this beautiful and straightforward simplicity, because your ability to get simple notions was lost over the years of your mathematical sophisticated training.

So is the case of a line or a point, they are undefined terms, and understood according different context dependent axiomatic systems that there is no common basis between them accept that they are using the words "Line" and/or "Point".

In other words, there is no generalization of these concepts according to the context dependent paradigm.

Since most of the axiomatic systems are using sets, then the concept of Line is not an
atom, but it is a thing that is defined by other building-blocks (you can call them points or not, but it does not change the fact that a line is not an atom by standard Math.)


Professional mathematicians do not afraid to use Lines and points as related object (only people that have troubles with their abstract abilities avoid it).

For example:

1. Why set theory?

Why do we do set theory in the first place? The most immediately familiar objects of mathematics which might seem to be sets are geometric figures: but the view that these are best understood as sets of points is a modern view. Classical Greeks, while certainly aware of the formal possibility of viewing geometric figures as sets of points, rejected this view because of their insistence on rejecting the actual infinite. Even an early modern thinker like Spinoza could comment that it is obvious that a line is not a collection of points (whereas for us it may hard to see what else it could be) (Ethics, I.15, scholium IV, 96).

http://www.seop.leeds.ac.uk/entries/settheory-alternative/

Prof. Randall Holmes (http://math.boisestate.edu/~holmes/ )


Hilbert: I.1: Two distinct points A and B always completely determine a straight line a. ...
( http://en.wikipedia.org/wiki/Hilbert's_axioms )

Well, Hilbert is wrong, because a non-local element like a line cannot be completely determined by local elements like points.

I explicitly show it by using Symmetry as the basis of non-locality and Asymmetry as the basis of locality.

Furthermore, I explicitly show that Symmetry/ Asymmetry is the basis of Logic itself.

It is rigorously written in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .

 

[doronshadmi]

And we are lucky that mathematics is able to transcend the restrictions you slap on it.

On the contrary.

The completeness of a researchable thing is exactly its restriction.

 

[Apathia]

On the contrary.

The completeness of a researchable thing is exactly its restriction.

You are missing the irony that your "Incompleteness" is denying Mathematics the ability to work with Infinity as a real concept. You lose the dynamic that is at the base of Calculus, Transfinite Numbers, Godel's Incompleteness Theorm, and the math modern physics depends upon.

Think again. You are undermining what you really want to achieve.

 

[jsfisher]

A number is the simplest building-block of the researchable.

So, we can just ignore geometry (in its several forms), topology, set theory, logic and several other branches of Mathematics for their lack of numbers.

Curious, isn't it though, that this alleged most fundamental building block, the number, is not that basis of your pet theory.

Your sophisticated manipulations of that building-block, do not allow you to get this beautiful and straightforward simplicity, because your ability to get simple notions was lost over the years of your mathematical sophisticated training.

I don't believe in Santa Claus and the Tooth Fairy any more either.

So is the case of a line or a point, they are undefined terms, and understood according different context dependent axiomatic systems that there is no common basis between them accept that they are using the words "Line" and/or "Point".

Ah! So you have changed your position on the definition of line?

Since most of the axiomatic systems are using sets, then the concept of Line is not an
atom, but it is a thing that is defined by other building-blocks (you can call them points or not, but it does not change the fact that a line is not an atom by standard Math.)

You've gone full circle in a single post. How every efficient of you. You are back to your flawed belief about the definition of a line. Got any evidence to support that?

...
Hilbert: I.1: Two distinct points A and B always completely determine a straight line a. ...
( http://en.wikipedia.org/wiki/Hilbert's_axioms )

Well, Hilbert is wrong, because a non-local element like a line cannot be completely determined by local elements like points.

Poor Hilbert. Undone by a 5 year-old.

I explicitly show it by using Symmetry as the basis of non-locality and Asymmetry as the basis of locality.

No, all you have done is constructed your own person vocabulary and used it to construct gibberish.

Furthermore, I explicitly show that Symmetry/ Asymmetry is the basis of Logic itself.

Ditto.

It is rigorously written in http://www.geocities.com/complementarytheory/NXOR-XOR.pdf .

Ditto.

 

[doronshadmi]

So, we can just ignore geometry (in its several forms)

On the contrary.

You have to re-examine the foundations of the mathematical science in order to define something that is even simpler than Symmetry\Asymmetry complementation.

There is no doubt that the mathematical science of the past 2500 years is based on undefined fundamental concepts like Line, Point, Number, Non-Finite etc.

The context dependent paradigm is the result these undefined fundamental concepts.

At the moment that these fundamental concepts are defined, then and only then the mathematical science is changed by a paradigm shift and becomes the organic framework that each part of it feeds and be fed by the rest of the parts as a one comprehensive method, which is developed according to the laws of evolution.

This paradigm-shift cannot be done if the difference between the researchable and the non-researchable is not understood, and this understanding cannot be achieved unless the mind is not aware of itself as an inseparable factor of this understanding.


When the consciousness is awaken to its own abilities the Phoenix effect is inevitable because of the consciousness' inventible power.

 

[jsfisher]

On the contrary....

You don't even understand your own posts, do you.

You said, "a number is the simplest building-block of the researchable." I commented on that because (1) the number is not the basis for all symmetry\asymmetry complementation gibberish you spew, and (2) so many things in Mathematics have no basis in numbers.

Now, you contradict yourself (again).

 

[jsfisher]

When the consciousness is awaken to its own abilities the Phoenix effect is inventible.

This typographic error is so appropriate.

 

[doronshadmi]

You are missing the irony that your "Incompleteness" is denying Mathematics the ability to work with Infinity as a real concept.

Not at all.

The real concept of infinity (what is called actual infinity) is total simplicity.

This simplicity is the common ground of anything that is not total simplicity.

As a result infinitely many things are able to be developed as organs of a one comprehensive realm, that no part of it is totally complete and therefore change and can be changed forever according to the non-arbitrary laws of Evolution.

The realm of the researchable is the realm where the total and the unchanged expresses itself by infinitely many creative and unexpected ways that must be incomplete in order to be expressed.

 

[doronshadmi]

You don't even understand your own posts, do you.

You said, "a number is the simplest building-block of the researchable." I commented on that because (1) the number is not the basis for all symmetry\asymmetry complementation gibberish you spew, and (2) so many things in Mathematics have no basis in numbers.

Now, you contradict yourself (again).

My definition of Number is not what you (by using the current paradigm) call a number.

This building-block is called the Organic Natural Number, and it is the the simplest building-block of Symmetry\Asymmetry complementation (the reseachable).

You still try to understand a paradigm-shift in terms of the old paradigm, and you fail.

 

[doronshadmi]

This typographic error is so appropriate.

Yes. I forgot to write the last part of it.

Please read it again.

 

[jsfisher]

My definition of Number is not what you (by using the current paradigm) call a number.

This surprises no one. We've come to expect that what you mean has nothing to do with what you actually say. Having your own private vocabulary is a major part of all that.

This building-block is called the Organic Natural Number, and it is the the simplest building-block of Symmetry\Asymmetry complementation (the reseachable).

You are still trying to avoid the obvious. So, instead you contradict yourself. Your framework doesn't use the number as a fundamental building-block; it is a result (that follows after pages of gibberish). Moreover, the number (be it organic or inorganic) is not the basis of many, many branches of Mathematics.

You still try to understand a paradigm-shift in terms of the old paradigm, and you fail.

Yeah, all that insistence we have for words having meaning and standard terminology...that's just so third grade!

 

[doronshadmi]

Your framework doesn't use the number as a fundamental building-block; it is a result

Ok. English problems.

Let's do it like this:

You have a reseachable realm.

The simplest thing that is also reseachable (and I call it the building-block of the researchable, which is not the non-reseachable) is defined by the Organic Naturel Number.

You may say that I said that the researchable cannot be researched by the researchable.

Well ONN is not used to reserach the researchable, but it is the researchable at it most basic form.

the number (be it organic or inorganic) is not the basis of many, many branches of Mathematics.

There is no such general thing as number in standard Math, so please save your words.

 

[jsfisher]

You have a reseachable realm.

The simplest thing that is also reseachable (and I call it the building-block of the researchable, which is not the non-reseachable) is defined by the Organic Naturel Number.

Yes, that is just about what you said before. You are still contradicting yourself. By the way, you presuppose the existence of both (standard) numbers and arithmetic in your ONN treatise. That makes your organic numbers more like compost than anything more substantive.

You may say that I said that the researchable cannot be researched by the researchable.

I am reasonably certain I would never say such a thing.

Well ONN is not used to reserach the researchable, but it is the researchable at it most basic form.

Good to know.

There is no such general thing as number in standard Math, so please save your words.

Yet another absurdity for the list!

 

[Apathia]

Not at all.

The real concept of infinity (what is called actual infinity) is total simplicity.

This simplicity is the common ground of anything that is not total simplicity.

As a result infinitely many things are able to be developed as organs of a one comprehensive realm, that no part of it is totally complete and therefore change and can be changed forever according to the non-arbitrary laws of Evolution.

The realm of the researchable is the realm where the total and the unchanged expresses itself by infinitely many creative and unexpected ways that must be incomplete in order to be expressed.

I think I get what you are aiming at here, but your arrow is unable to reach its mark.