Cont: Deeper than primes - Continuation 2

[doronshadmi]

Doronshadmi has a unique perspective on notation.

Once more your partial use of your brain skills (their verbal-symbolic-only skills) fails to comprehend awareness that links visual_spatial AND verbal_symbolic brain skills into one comprehensive realm that is aware of itself and it is not the sum of its expressions.

I predict you will soon be treated to a convoluted monologue of the meta-physical meaning of braces used in conventional set notation.

I will also predict the word, consciousness, new to Doron's repertoire, will be added to and prominently placed in the recycled word salad you have summoned.

You predict nothing, because it is already given in http://www.internationalskeptics.com/forums/showpost.php?p=11784784&postcount=2691 and http://www.internationalskeptics.com/forums/showpost.php?p=11848541&postcount=2712.

You simply can't comprehend it by partially using your brain skills, and as a result it is always a part of your future (your "I will ..." is the best that you currently can get).

 

[Hevneren]

It is not about missing members, but about the inaccessibility of endless expressions between the outer "{" and "}", to the outer "{" and "}".

Why, then, did you mention missing members? And what do you mean with this inaccessibility? A human can see what's between a pair of brackets, but the brackets themselves obviously can't "access" it. What does that even mean?

 

[doronshadmi]

Why, then, did you mention missing members?

I actually said that no member is missing.

And what do you mean with this inaccessibility?

In means the no amount of members is the outer "{" and "}".

A human can see what's between a pair of brackets, but the brackets themselves obviously can't "access" it.

The brackets themselves are obviously irreducible into what may be found between them, and this is exactly the meaning of {x}, both visually AND symbolically.

What does that even mean?

It means that we actually live in a self-aware non-entropic realm, which has no limits for further development of its expressions (it is not the sum of its expressions).

 

[doronshadmi]

recycled word salad

This is indeed the best that one can get by using only his verbal_symbolic brain skills in order to comprehend the issue at hand.

 

[Hevneren]

I actually said that no member is missing.

My point is that no members can ever miss from any set, ever. If you "remove" a member, you have a different set that isn't missing any members. So why even mention the possibility?

In means the no amount of members is the outer "{" and "}".

No, obviously not. The braces are just symbols. They aren't supposed to "be" the set members.

The brackets themselves are obviously irreducible into what may be found between them, and this is exactly the meaning of {x}, both visually AND symbolically.

How about this: The left brace means "here comes a set". The right brace means "ok, that was the set". You seem to be overthinking this.

It means that we actually live in a self-aware non-entropic realm, which has no limits for further development of its expressions (it is not the sum of its expressions).

Epic non sequitur, see above.

 

[doronshadmi]

My point is that no members can ever miss from any set, ever. If you "remove" a member, you have a different set that isn't missing any members. So why even mention the possibility?

You still do not get the concept of set both visually AND symbolically, and as a result you understand only by its members.

No, obviously not. The braces are just symbols. They aren't supposed to "be" the set members.

No, the braces are the visual_spatial aspect of the concept of set, which are inaccessible to any collection of members between them. Since you get the concept of set only in terms of your verbal_symbolic brain skills, you are still missing the visual_spatial AND verbal_symbolic understanding of the concept of set.

How about this: The left brace means "here comes a set". The right brace means "ok, that was the set".

This is how one understands the concept of set sequentially exactly because he\she uses only his\her verbal_symbolic brain skills.

You seem to be overthinking this.

You seem to use only your verbal_symbolic brain skills in order to comprehend the issue at hand.

Epic non sequitur, see above.

Your visual_spatial AND verbal_symbolic brain skills are given you naturally for free (no "Epic non sequitur" or any kind of drama are involved here) and yet you choose to use only your verbal_symbolic brain skills in order to understand the issue at hand, and a result the best you get is indeed "Epic non sequitur".

 

[Hevneren]

This is how one understands the concept of set sequentially exactly because he\she uses only his\her verbal_symbolic brain skills.

You know nothing about how I understand the concept of sets. I was talking about the braces. They are symbols, so it's totally appropriate to use what you call "verbal_symbolic brain skills" on them.

Do you see the difference between a concept and a symbol?

 

[Hevneren]

... both visually AND symbolically...

...you are still missing the visual_spatial AND verbal_symbolic understanding...

...Your visual_spatial AND verbal_symbolic brain skills are given you ...

Please, Doron, stop using the term "visual_spatial AND verbal_symbolic" as it were some kind of superpower of yours. It isn't, and you actually know nothing about how other people use their brains.

 

[doronshadmi]

They are symbols,

To one that gets everything only in terms of his her verbal_symbolic brain skills.

 

[doronshadmi]

Please, Doron, stop using the term "visual_spatial AND verbal_symbolic" as it were some kind of superpower of yours.

The ability to use both visual_spatial AND verbal_symbolic brain skills is naturally given for free to anybody. No superpowers of any kind are involved.

It isn't, and you actually know nothing about how other people use their brains.

You give me all the needed information in order to understand that you understand the issue at hand by being focused only on your verbal_symbolic skills of the issue at hand.

Please look at https://www.youtube.com/watch?v=sMNwA4qbcGY.

What is called there the right hemisphere is called by me visual_spatial brain skills.

What is called there the left hemisphere is called by me verbal_symbolic brain skills.

A normal brain function is not less than the smooth linkage among the right AND the left hemispheres into one unified conspicuousness also during math work.

This fundamental awareness is deeper than primes.

 

[doronshadmi]

The "unified conspicuousness" in the previous post has to be corrected to "unified consciousness"

 

[doronshadmi]

By being aware of https://c1.staticflickr.com/4/3929/15309487328_d8023ed9f0_b.jpg one actually aware that contradiction and tautology (the basis of logic) are inseparable of each other, where also Bose-Einstein and Fermi-Dirac functions are inseparable of each other (the basis of Physics).

Moreover, actually the basis of logic and physics are inseparable of each when https://c1.staticflickr.com/4/3929/15309487328_d8023ed9f0_b.jpg is taken both visually AND verbally (the two brain hemispheres (our main lenses) are inseparable of each other in such awareness, which is actually the non-composed (Unity) whether it is vibrating or calm, such that no amount of vibrations is Unity (the non-composed) in itself.

The irreducibility of life into its components is exactly Unity consciousness, which is not the sum of its infinitely many levels of vibrations, exactly because it is non-composed, whether it expresses itself (vibrating) or not (stays calm (the analogy of the cross' vibrations endless non-composed straight-line)).

The mechanical awareness of reality (whether it is taken logically, physically, or biologically) is simply the illusion that things can actually be separated of each other, and it is always the result of partially using one's brain skills, such that he\she is unaware of his\her non-composed substance during daily life (during vibrations).

One's uniqueness (some vibration) is actually given by vibrations' inseparability.

 

[doronshadmi]

Undestanging set by using visual_spatial AND verbal_symbolic brain skills

Let's take, without loss of generality, the given diagram by using visual_spatial AND verbal_symbolic brain skills:

In that diagram the constant non-composed orange figure (straight or bent) is equivalent to the outer "{" and "}" of what is defined as set.

The empty set {} is equivalent to the straight orange figure, which has no bending.

A member is some bend among the constant orange figure, which does not change it into a composed figure, since no point on the orange figure is composed.

By using visual_spatial AND verbal_symbolic brain skills in case of the given diagram, the notion of constant non-composed orange figure among any amount of bent figures, is given be the set {{}//4¹, {}//4², {}//4³, ...}, which is obviously bijective with set {1, 2, 3, ...}, where {}//4ⁿ expression means that {} is a constant non-composed figure under any amount of bending.

Since {} is non-composed, whether it is straight or bent, no amount of its non-composed figures defines it as a composed figure, therefore it is not the sum of the convergent projected 2(a+b+c+d+...) among it, which is equivalent to the inaccessibility of 1,2,3,... to the outer "{" and "}" in {1, 2, 3, ...}, known as the set of natural numbers.

The inaccessibility of 1,2,3,... to the outer "{" and "}" prevents the definition of fixed size like aleph⁰ to an infinite amount of members between the outer "{" and "}", and such understanding is available only by using visual_spatial AND verbal_symbolic brain skills.

Actually, by using visual_spatial AND verbal_symbolic brain skills one understands the linkage between the inability to define the constant non-composed X>0 by the convergent series 2(a+b+c+d+...) AND the inability to define the amount of set {1, 2, 3, ...} by a fixed value like aleph⁰.

This inability is exactly the non-entropic realm, which has no limits for further development of its expressions, because no amount of expressions is the non-composed.

 

[doronshadmi]

Another way to spatially AND verbally define the outer "{" and "}" in case of the considered diagram is {{}//4¹, {}//4², {}//4³, ...}//4⁰ (the straight figure is not one of its members).

In case that the considered set is {{}//4⁰, {}//4¹, {}//4², {}//4³, ...}, the outer "{" and "}" is equivalent to an endless non-composed straight figure, which is inaccessible to any amount of its members (can't be defined in terms of collection of members, no matter what members or how many of them are involved).

More about it is already given in http://www.internationalskeptics.com/forums/showpost.php?p=11856790&postcount=2732.

 

[doronshadmi]

By using visual_spatial AND verbal_symbolic brain skills, no collection is its non-composed substance such that without loss of generality the axiom of mathematics is:

Given X (the non-composed), no sub-X (collections) is X (the non-composed).

By being aware of the non-composed among its collection of expressions, Unity consciousness is aware of itself as the substance of unlimited (endless) new expressions, and this is exactly what Life is as an open (unlimited) non-entropic realm (as briefly given in http://www.internationalskeptics.com/forums/showpost.php?p=11856790&postcount=2732).

The current verbal_symbolic-only mathematics, is actually an entropic and therefore closed realm, that defines a convergent series by a given limit or an endless collection by a fixed value.

By doing so current verbal_symbolic-only mathematics misses Life which is actually beyond AND among its expressions (it is open since it is not limited by its expressions).

 

[doronshadmi]

Useful science is actually done by achieving results that can be tested and used beyond some particular observation.

It means that the observation is not-one-of-many observation, which naturally can be used as the substance of any one-of-many observation.

I find Mathematics as the exact tool that enables the natural linkage among not-one-of-many observation AND one-of-many observation.

In order to actually be such a tool, mathematicians can't partially use their brain during mathematical activity.

Unfortunately for the past 250 yeas almost only verbal-symbolic brain skills are used among mathematicians during mathematical activity, which means that modern mathematics is actually based on one-of-many observation (some particular observation).

In order to correct it, both visual_spatial AND verbal_symbolic brain skills have to be used during mathematical activity.

For example, let's use both visual_spatial AND verbal_symbolic brain skills in order to define the natural linkage among not-one-of-many observation AND one-of-many observation.

The minimal amount of one-of-many things is two things.

Question: What enables the knowledge that there are two things, in the first place?

By using verbal_symbolic brain skills, this question is not asked at the basis of fundamental mathematical concept like Set, where {5,pi} is some example (without loss of generality) of two things, and the outer "{" and "}" is not defined.

So by modern mathematics (which is mostly verbal_symbolic_only framework) the ability to gather at least things is arbitrarily done.

A simple visual_spatial AND verbal_symbolic tool, which naturally enables to answer to this question (by also define the outer "{" and "}" as an essential thing of fundamental mathematical concept like Set), is Möbius strip:

By partially observe it, it has two edges (represented here by brown color), where each edge is one-of-many thing.

This observation is actually possible because also global observation is done, which provides the knowledge that there is one edge along the Möbius strip (which is not-one-of-many thing) where this knowledge is represented by the the outer "{" and "}" (which is not any one-of-many thing between them).

The visual_spatial knowledge of not-one-of-many thing (represented here by one edge along the Möbius strip), which is also represented by the outer "{" and "}", actually enables to gather one-of-many things like 5,pi into a set (for example: {5,pi}).

So, fundamental mathematical concept like Set is not rigorously defined, unless both visual_spatial AND verbal_symbolic brain skills are used, as actually demonstrated in this post.

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

Generally, one's awareness is fully activated only by simultaneously using his\her visual_spatial AND verbal_symbolic brain skills.

Without it, no actual scientific progression is possible.

 

[Little 10 Toes]

 

[doronshadmi]

[qimg]https://imgs.xkcd.com/comics/communicating.png[/qimg]

"Still focused only on misinterpretation of verbal_symbolic brain skills for nice little joke, where the visual_spatial aspect is used here just for decoration" said Alice "and, by the way, I am thinner than my representation in that drawing" she added.

 

[doronshadmi]

Any way, the model of Möbius strip naturally demonstrates the linkage among being aware of one thing at once (the visual_spatial brain skill) as the substance of being aware of multiple things step-by-step (the verbal_symbolic brain skill).

Moreover this awareness (known also as Unity consciousness) is exactly the core of useful scientific work that actually achieving results that can be tested and used beyond some particular observation.

Furthermore, the observed, the observer and the tool of observation are actually one thing, which is not the sum of its expressions, and as a fundamental result we get non-entropic realm, which is essentially open to new expressions (infinitely many things can't be defined by a fixed limit, fixed cardinality, etc.).

 

[doronshadmi]

ℵ₀ is defined as the smallest cardinal number greater than any given finite cardinal number.

The infinite binary tree has ℵ₀ levels, such that any cardinal number (represented by positional notation, where the radix point is placed at the ℵ₀ level) has its own unique path of ℵ₀ 0;1 bits in this tree (every number is distinguished of the rest of the numbers).

By carefully observe the infinite binary tree, it is not hard to find more than one unique cardinal number represented by ℵ₀ 0;1 bits, which is greater than any given finite cardinal number, for example:

Cardinal number 1100... (the radix point is placed at the ℵ₀ level),
Cardinal number 0101... (the radix point is placed at the ℵ₀ level),
Cardinal number 0010... (the radix point is placed at the ℵ₀ level),
...

Please observe the given diagram in The Infinite Binary Tree.

Its order starts with the path of ℵ₀ 0 bits (cardinal number ...000.) and ends with the path of ℵ₀ 1 bits (cardinal number 111...), where the radix point is placed at the ℵ₀ level in both cases.

Question 1: What is the unique cardinal number taken from such representation of infinite cardinal numbers, which is the smallest cardinal number greater than any given finite cardinal number (this unique cardinal number is also known by the name ℵ₀)?

Question 2: Are cardinal numbers like 1100... (the radix point is placed at the ℵ₀ level) or 0101... (the radix point is placed at the ℵ₀ level) etc. can be used in order to define sizes that are greater than ℵ₀ and smaller than 2^ℵ₀?

One may claim that the answers are depend on what ordering is placed on the tree. Since the existence of a well ordering of these paths depends on the axiom of choice, it means that one can't get an explicit one.

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

If one carefully observes the diagram that represents some part of the "top" of The Infinite Binary Tree (where according to Contemporary mathematics, each district path of it is constructed by ℵ₀ bits taken as a whole, and represent some cardinal number by positional notation (where the radix point is placed at the ℵ₀ level of that tree)) one realizes that its left and right sides are complements of each other.

For example:

The complement of the finite cardinal number 000...000. is the infinite cardinal number 111...111.

The complement of the finite cardinal number 000...001. is the infinite cardinal number 111...110. (which is the immediate predecessor of the infinite cardinal number 111...111.)

The complement of the finite cardinal number 000...010. is the infinite cardinal number 111...101. (which is the immediate predecessor of the infinite cardinal number 111...110.)

The complement of the finite cardinal number 000...011. is the infinite cardinal number 111...100. (which is the immediate predecessor of the infinite cardinal number 111...101.) ... etc. such that:

000...000. < 000...001. < 000...010. < 000...011. ... < ... 111...100. < 111...101. < 111...110. < 111...111.

So by using an accurate value like ℵ₀ in order to define an infinite cardinal number, one actually discovers (because of this accuracy) that infinite cardinal numbers are actually distinguished of each other by finite sizes (for example: ℵ₀ < ℵ₀+1 exactly by 1).

So by using an accurate value like ℵ₀ in order to define an infinite cardinal number, ℵ₀ = ℵ₀+1 is actually false exactly because ℵ₀ is accurate (measures collection of things as a whole).

I wish to clarify something about the issue at hand.

Whole is not the same as All (or Complete), which means that the size (the cardinality) of a given thing can be changed without changing its wholeness, for example: A given tree is growing without changing its, so called, organic wholeness.

Another example: Wholeness, in case of endless growing or endless shrinking circle is its invariant ratio between its circumference and its diameter, known as Pi.

In the case of The Infinite Binary Tree the complementary relationship between its left and it right sides is invariant during its growth.

Adding, for example, 1 not at its most right path (represented by 111...111.) does not add new level to The Infinite Binary Tree, and if more levels are added, it does not change the complementary relationship between its left and its right sides.

"if n is in S, then n+1 is in S" defines an ever growing S as a whole, where ℵ₀ actually measures S wholeness and not S completeness.

Complete things are invariant-only, where whole things are both variant AND invariant (as given in the examples above) without getting into contradiction, as complete things do exactly because they are invariant-only.

Currently the majority of mathematicians define, for example, N in terms of completeness (actual infinity) and not in terms of wholeness (potential infinite), exactly because they are doing mathematics that its results are derived from their verbal-symbolic_only brain skills, instead of using both their verbal-symbolic AND visual-spatial brain skills in order to get valid mathematical results.