Deeper than primes - Continuation

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zooterkin said:
You got that from the preface to a book? Wow. I wonder what you'd get if you read the book itself.
Click to expand...
The book itself is focused on the visual_spatial aspect of the considered subject, according to the following quote:
In this book, it is our purpose to give a presentation of geometry, as it stands today, in its visual, intuitive aspects. With the aid of visual imagination we can illuminate the manifold facts and problems of geometry, and beyond this, it is possible in many cases to depict the geometric outline of the methods of investigation and proof, without necessarily entering into the details connected with the strict definitions of concepts and with the actual calculations.
Click to expand...


My work is a unification of verbal_symbolic AND visual_spatial reasoning (the two mentioned tendencies in the preface).

I wonder what you'd get if you read http://www.scribd.com/doc/97823738/Unity-Awarness and http://www.scribd.com/doc/98276640/Umes by using your verbal_symbolic AND visual_spatial brain skills.
 
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doronshadmi said:
How to unify the verbal_symbolic AND visual_spatial reasoning (the two mentioned tendencies).
Click to expand...


And, yet, you are the only person in this thread who repeatedly shows you are unable to do just that. Hilbert writes about using the visual aspects of geometry to appeal to ones intuition to outline methods of reasoning and proof--not a substitute for formality, but a crutch to help better understand it. You, on the other hand, start with things misrepresented pictorially, then conclude your unique interpretation trumps reality. Contradiction is simply reality's failure to "get it" in your bizarre world.

Give it up, doron. Your reading comprehension is poor. Your logic skills are minimal, and nonexistent when more than one step is involved. Abstract thinking is beyond you. Your visual/spatial reasoning skills are dysfunctional.

To top it off, you stuff doesn't work.
 
jsfisher said:
And, yet, you are the only person in this thread who repeatedly shows you are unable to do just that. Hilbert writes about using the visual aspects of geometry to appeal to ones intuition to outline methods of reasoning and proof--not a substitute for formality, but a crutch to help better understand it. You, on the other hand, start with things misrepresented pictorially, then conclude your unique interpretation trumps reality. Contradiction is simply reality's failure to "get it" in your bizarre world.

Give it up, doron. Your reading comprehension is poor. Your logic skills are minimal, and nonexistent when more than one step is involved. Abstract thinking is beyond you. Your visual/spatial reasoning skills are dysfunctional.

To top it off, you stuff doesn't work.
Click to expand...

This is the main issue, IMO. If only he could show some tangible result he arrived at by using his "stuff" (yeah, that's the correct word, not work).
 
Traditional mathematicians here living is a bizarre realm of formalism that is derived from verbal_symbolic-only brain skills (their abstraction abilities is limited only to verbal_symbolic brain skills, and the last example is their inability to get Knot set theory ( http://www.internationalskeptics.com/forums/showpost.php?p=8421119&postcount=1628 )) .

From the point of view of this bizarre realm they simply can't comprehend formalism that is derived from verbal_symbolic AND visual_spatial brain skills.

This thread is a reliable demonstration of the considered subject.
 
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Ok, for better communication about Knot set theory, let us use the term rope instead of knot.

According to Knot set theory, a rope (whether it is open or closed) is first of all a set.

Since a given rope (whether it is closed or open) is first of all a set (notated, for example, as A), then being a member is any given rope that is located under A, no matter if the over/under relations are involved with knots, or not.

A rope can be abstracted into 1-dimesional space, yet what is written above, holds.
 
doronshadmi said:
Ok, for better communication about Knot set theory, let us use the term rope instead of knot.

According to Knot set theory, a rope (whether it is open or closed) is first of all a set.

Since a given rope (whether it is closed or open) is first of all a set (notated, for example, as A), then being a member is any given rope that is located under A, no matter if the over/under relations are involved with knots, or not.

A rope can be abstracted into 1-dimesional space, yet what is written above, holds.
Click to expand...


Although word substitution is your forte, Doron, it doesn't improve things.
 
doronshadmi said:
The book itself is focused on the visual_spatial aspect of the considered subject, according to the following quote:



My work is a unification of verbal_symbolic AND visual_spatial reasoning (the two mentioned tendencies in the preface).
Click to expand...
Perhaps you could point to where those terms are mentioned in the preface?

You do realise that the authors of that book were "traditional" (I'd prefer the term "real") mathematicians?
 
Prof. Kauffman does not use sets in the traditional way, for example, please look at the following Knot set theory expressions:

Code: 
       a                                                      
                                               ┌─────┐        
       │                                       │     │        
     ─────┐         a┌──────┐    ┌────┐    a─────────│──┐     
       │  │          │      │    │    │        │     │  │     
       └──────┐      │      │    │ a──┘        │     │  │     
          │   │      └──────┘    │             │     │  │     
          └───┘        a={}        a={}        │     └──│───  
        a={a,a}                                │        │     
                                               └────────┘     
                                                 a={a,a,a}    
       a                 ┌─────┐                              
                         │     │                              
       │             a─────────│──┐        a─────────┐        
   b ──│──┐              │     │  │            b┌──────────┐  
       │  │              │     │  │             │    │     │  
       └──────┐          │     │  │             │    │     │  
          │   │          │     └──│───b         │    │     │  
          └──                     │             └──────────┘  
        a={b,b}            ───────┘         ─────────┘        
                           a={b,b}               a={}         
                           b={a}                 b={a,a}

As you can see, a member is defined as a rope under rope, according to these expressions, which are derived from verbal_symbolic AND visual_spatial reasoning.
 
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zooterkin said:
Perhaps you could point to where those terms are mentioned in the preface?

You do realise that the authors of that book were "traditional" (I'd prefer the term "real") mathematicians?
Click to expand...
He uses the term "visual imagination".

Again, my work is a unification of verbal_symbolic AND visual_spatial reasoning (the two mentioned tendencies in the preface are not unified by the traditional view of this fine subject).

So once again, I wonder what you'd get if you read http://www.scribd.com/doc/97823738/Unity-Awarness and http://www.scribd.com/doc/98276640/Umes by formally using your verbal_symbolic AND visual_spatial brain skills in terms of formal unification, and not just as informal visual outlines that have to be formalized by verbal_symbolic reasoning.
 
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doronshadmi said:
He uses the term "visual imagination".
Click to expand...
Indeed he does. Which is not what I asked about.
Again, my work is a unification of verbal_symbolic AND visual_spatial reasoning (the two mentioned tendencies in the preface are not unified by the traditional view of this fine subject).
Click to expand...
Where does the preface refer to either of your made-up terms?
 
I forgot to add b={} in the lower left expression, here is the correct one:

Code: 
       a                                                      
                                               ┌─────┐        
       │                                       │     │        
     ─────┐         a┌──────┐    ┌────┐    a─────────│──┐     
       │  │          │      │    │    │        │     │  │     
       └──────┐      │      │    │ a──┘        │     │  │     
          │   │      └──────┘    │             │     │  │     
          └───┘        a={}        a={}        │     └──│───  
        a={a,a}                                │        │     
                                               └────────┘     
                                                 a={a,a,a}    
       a                 ┌─────┐                              
                         │     │                              
       │             a─────────│──┐        a─────────┐        
   b ──│──┐              │     │  │            b┌──────────┐  
       │  │              │     │  │             │    │     │  
       └──────┐          │     │  │             │    │     │  
          │   │          │     └──│───b         │    │     │  
          └──                     │             └──────────┘  
        a={b,b}            ───────┘         ─────────┘        
        b={}               a={b,b}               a={}         
                           b={a}                 b={a,a}

As you can see, a member is defined as a rope under rope, according to these expressions, which are derived from verbal_symbolic AND visual_spatial reasoning.

Also according to this reasoning a member of a given set is not identical to the set, since a set is any given rope (notated by the outer "{" and "}"), where a member is a rope under a given rope.

Also in the case of a={b} and b={a} a or b as sets are not the same as a or b as members of a given set.

So Russell's paradox is avoided by Knot set theory.
 
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zooterkin said:
Indeed he does. Which is not what I asked about.

Where does the preface refer to either of your made-up terms?
Click to expand...

The preface gets "visual imagination" as no more than an "outline of the methods of investigation and proof", or in other words, "visual imagination" is not taken in terms of formal reasoning.

On the contrary I take "visual imagination" as formal reasoning that complements the verbal_symbolic formal reasoning.

So once again, I wonder what you'd get if you read http://www.scribd.com/doc/97823738/Unity-Awarness and http://www.scribd.com/doc/98276640/Umes by formally using your verbal_symbolic AND visual_spatial brain skills in terms of formal unification, and not just as informal visual outlines that have to be formalized by verbal_symbolic reasoning.

http://www.internationalskeptics.com/forums/showpost.php?p=8440898&postcount=1655 was done by an accepted mathematician that knows how to formally use verbal_symbolic AND visual_spatial brain skills in terms of formal unification.
 
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doronshadmi said:
As you can see, a member is defined as a rope under rope, according to these expressions, which are derived from verbal_symbolic AND visual_spatial reasoning.
Click to expand...


And yet, Kauffman never defined membership in any such way. That's just something Doron made up then lied about.

But, heck, I can make pretty diagrams, too. Doron is so much more comfortable arguing diagrammatic trivialities while completely missing any substance.

Code: 
      ┌─────┐              ┌─────┐        
      │     │              │     │        
  a─────────│──┐       a─────────│──┐     
      │     │  │           │     │  │     
      │     │  │           │     │  │     
      │     │  │           │     │  │     
      │     └──│───        │     └──────  
      │        │           │        │     
      └────────┘           └────────┘     
      a={a,a,a}            a={a,a,a}
 
Now the traditional mathematicians here demonstrate their inability to understand the redundancy among the members of the expression a={a,a,a}, such that set a is the rope in itself (notated by the outer "{" and "}"), where no one of the redundant members are the rope in itself, no matter how the rope interacts with itself (no one of the redundant members is at the level of the set).

They simply do not understand the following verbal_symbolic AND visual_spatial expressions (the left rope has a knot, where the right rope does not have a knot, but in both cases the set and the members are in different levels, notated as a={a,a,a}):
Code: 
      ┌─────┐              ┌─────┐        
      │     │              │     │        
  a─────────│──┐       a─────────│──┐     
      │     │  │           │     │  │     
      │     │  │           │     │  │     
      │     │  │           │     │  │     
      │     └──│───        │     └──────  
      │        │           │        │     
      └────────┘           └────────┘     
      a={a,a,a}            a={a,a,a}

exactly because their reasoning is limited to one level of verbal_symbolic-only\strict-only expressions, such that a set and a member of a given set are identical by this one level verbal_symbolic-only\strict-only reasoning.

They can make pretty diagrams, while completely missing any substance of the considered subject, by using their one level verbal_symbolic-only\strict-only reasoning.

For example, by their one level (flat) verbal symbolic-only\strict-only reasoning, they can't realize that Knot set theory avoids Russell's paradox.
 
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The following ropes are the same set (notated by the outer "{" and "}"), even if the left rope is closed and the right rope is open:

Code: 
               a ┌──────┐    ┌────┐          
                 │      │    │    │                       
                 │      │    │ a──┘              
                 └──────┘    │              
                   a={}        a={}

The traditional mathematicians here can't comprehend that.
 
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Prof. Kauffman confirms what I say about sets and members, according Knot set theory, in two different posts:

7548959764_6d33009697_b.jpg


7549065322_5316bff35b_b.jpg


Here is the diagram that its link was given in the last post, in order to get Prof. Kauffman's confirmation about sets and members:

7535200760_aa2507a20d.jpg
 
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Hey Doron, have you shown the prof this thread or your "articles"? Are you afraid he's going to concur and recommend medication for you?
 
Once again it is shown that the traditional mathematicians here get the term Definition only if it is expressed by verbal_symbolic brain skills ("a passes under b" = "a is a member of b" = a ε b can't be known by the traditional mathematicians here).

Furthermore, because of this brain limitation they can't get Prof. Kauffman's replies to my posts to him, on this subject.


http://www.internationalskeptics.com/forums/showpost.php?p=8442577&postcount=1658 and http://www.internationalskeptics.com/forums/showpost.php?p=8442762&postcount=1659 can be added to their failures' list.

Also the attached mails are beyond their mind:

7552082778_1fdd216055_b.jpg


As can be seen, Prof. Kauffman uses the terms "rope", "segment" and "segment A over segment B" in order to define B as a member of A (which is equivalent to my "rope under rope" ("rope B under rope A", in this case) in order to define B as a member of A).
 
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doronshadmi said:
Once again it is shown that the traditional mathematicians here get the term Definition only if it is expressed by verbal_symbolic brain skills ("a passes under b" = "a is a member of b" = a ε b can't be known by the traditional mathematicians here).

Furthermore, because of this brain limitation they can't get Prof. Kauffman's replies to my posts to him, on this subject.
Click to expand...


It's that reading comprehension thing, again, isn't it, Doron? You keep referring to things that nobody but you is even discussing at the moment to erect strawmen about things nobody said while you completely evade your errors from the starting point of your current tangled sequence of posts.

Doron, you said Kauffman defined membership in terms of these string diagrams of which you have grown so fond. You are wrong. He did not define membership in terms of string diagrams. He did not define membership in terms of above or below or under or over relationships. He did not define membership at all.

He did, however, show how an extended concept of set could be applied to knots and how that application could be represented diagrammatically. He used those diagrams to introduce concepts and ideas that could be related back to formal knot theory.

Your ability to see things that aren't there is truly remarkable, Doron. Your phenomenal skills at misunderstanding are independent of the method of expression.
 
doronshadmi said:
Prof. Kauffman confirms what I say about sets and members, according Knot set theory, in two different posts:

Image 1 link: http://farm9.staticflickr.com/8285/7548959764_6d33009697_b.jpg

Image 2 link:
http://farm9.staticflickr.com/8027/7549065322_5316bff35b_b.jpg

Here is the diagram that its link was given in the last post, in order to get Prof. Kauffman's confirmation about sets and members:

Image 3 link:
http://farm8.staticflickr.com/7261/7535200760_aa2507a20d.jpg
Click to expand...

Interesting that the two "screen shots" of two different messages have the exact same number of items in the Inbox, and that you ask the same exact question twice, but with different subject lines, and that the first screen shot has your message easily readable and formatted, but the second screen shot has blurry and unformatted text.

Also you said "Ok, for better communication about Knot set theory, let us use the term rope instead of knot."

Let's not do what you want. Let's use the correct terms, the correct way, correctly.
 
Little 10 Toes said:
Interesting that the two "screen shots" of two different messages have the exact same number of items in the Inbox, and that you ask the same exact question twice, but with different subject lines, and that the first screen shot has your message easily readable and formatted, but the second screen shot has blurry and unformatted text.
Click to expand...

The two posts were sent to Prof. Kauffman, where the second post used the content of the first post + Knot set expressions, in order to get feedback about Knot set theory concrete examples.

Prof. Kauffman replied to both posts, and his replies support my notions in both posts.

For some reason you ignore these simple facts.

Little 10 Toes said:
Also you said "Ok, for better communication about Knot set theory, let us use the term rope instead of knot."
Click to expand...
So, now you ignore http://www.internationalskeptics.com/forums/showpost.php?p=8444459&postcount=1666 .

Little 10 Toes said:
Let's not do what you want. Let's use the correct terms, the correct way, correctly.
Click to expand...
What you call "the correct way" is a reasoning that is derived from verbal_symbolic-only brain skills.

So, I'll say it once again in case that you have missed it:

This thread is mainly derived from my disagreement about the attempt to reduce formalism into verbal_symbolic-only brain skills.

Knot set theory is a concrete example of a theory that its formal definitions are expressed by using verbal_symbolic AND visual_spatial brain skills.

Traditional mathematicians do not accept visual_spatial formalism, because formalism for them is expressed only by verbal_symbolic brain skills, for example, as expressed by this quote: "He used those diagrams to introduce concepts and ideas that could be related back to formal knot theory."

As long as you agree with traditional mathematicians' limitation of Formalism, there is no communication between us.
 
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The traditional mathematicians here get nothing since they translate verbal_symbolic AND visual_spatial formalism in terms of verbal_symbolic-only formalism.
 
Theorem:
Being a set is different than being a member of a given set.

Proof:
(1) Let us suppose that being a set is the same as being a member of a given set.

(2) Every member of a given set is different than the rest of the members of that set.

(3) According to (2) each member can be represented by a unique code, where in the case of infinite collection of members, each unique code is an infinitely long sequence of symbols, for example:

{
...
...01001... ,
...11101... ,
...10110... ,
...11111... ,
...10101... ,
...
}

(4) The code of a set is defined by using Cantor's Diagonalization, which is different than the rest of the codes that represent its members (in this example the code of a given set is ...10000...).

(5) If a set is one of its own members, then its code (for example:...10000...) must appear in the collection of the unique codes, which represent the members of that set.

(6) But according to (4) the code of a set is defined by using Cantor's Diagonalization, and in this case the code that represents a given set is different than the rest of the codes that represent the members of a given set (the example ...10000... can't be considered as the code of a given set, if it is used to represent a member of that set.)

(7) According to (6) assumption (1) is false and we can conclude that being a set is different than being a member of a given set.

Q.E.D

Flagg resolution ( http://homepages.math.uic.edu/~kauffman/TimeParadox.pdf ) is actually the difference between, for example, code ...01111... that represents a given member, and code ...10000... that represents a given set, where Cantor's Diagonalization guarantees the difference between the code that represents a set, and the code that represents a member of a given set.
 
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doronshadmi said:
Theorem:
Being a set is different than being a member of a given set.
Click to expand...

What are you trying to say here? Since every set is a member of some other set, what you actually wrote is just wrong on the face of it. Are you perhaps trying to say that no set is a member of itself?

Proof:
(1) Let us suppose that being a set is the same as being a member of a given set.
Click to expand...

Ok, but since the theorem claim is unclear, its negation can be no better.

(2) Every member of a given set is different than the rest of the members of that set.
Click to expand...

This is not a precise statement. Did you mean that for any set S, if A is in S and B is in S then A is different from B? If so, your claim is false.

(3) According to (2) each member can be represented by a unique code, where in the case of infinite collection of members, each unique code is an infinitely long sequence of symbols, for example:

{
...
...01001... ,
...11101... ,
...10110... ,
...11111... ,
...10101... ,
...
}
Click to expand...

Even if (2) were meaningful, which it isn't, this does not follow from it.

(4) The code of a set is defined by using Cantor's Diagonalization, which is different than the rest of the codes that represent its members (in this example the code of a given set is ...10000...).
Click to expand...

Well, since you failed to establish (3), this isn't going to fly.

(5) If a set is one of its own members, then its code (for example:...10000...) must appear in the collection of the unique codes, which represent the members of that set.
Click to expand...

"If a set is one of its own members...". Is this suggestive of what your theorem statement should have been? Be that as it may, (4) failed for lack of foundation, so this fails as well. Moreover, the framework you've used presumes an enumerable infinity. You have no basis for that, either.

(6) But according to (4) the code of a set is defined by using Cantor's Diagonalization, and in this case the code that represents a given set is different than the rest of the codes that represent the members of a given set (the example ...10000... can't be considered as the code of a given set, if it is used to represent a member of that set.)
Click to expand...

Fails four words into it.

(7) According to (6) assumption (1) is false and we can conclude that being a set is different than being a member of a given set.
Click to expand...

You got here through a sequence of compounded failure, so it fails, too. But even if (6) had succeeded, all you would have shown is that there is something that isn't a member of the set. So what? Perhaps you wanted a theorem claim that there was no universal set. Is that what you meant?

Q.E.D
Click to expand...

It would seem not.
 
Doron,

People (including myself) have asked you multiple times for proof that your "organic mathematics" *does* anything meaningful. I'm going to take it a step further:

What, in the context of myself not being a mathematician, can your theory do for me? How will it make my life easier? How will it make my life better? I ask this because in some of your scribd documents you warn vaguely about the destruction of our way of life etc if organic mathematics is not adopted. Don't make me search for the quote, I have no desire to wade through that all over again.

If something is as profound as you say it is, tell me why I should care. Don't use a single variable, don't use a single mathematical equation or concept above middle school level. It's a belief of mine that if you truly understand a subject and it's truly applicable to someones life, that you should be able to explain it at a very low level and the subject should immediately grasp how this is going to change their life. I do it all the time in my field, boiling down extremely complicated chemical phenomena into simple, easy to understand talking points that convince endusers as well as investors.

So here's your chance. You've been fencing with mathematicians for over 40 pages in this thread alone. By your admission you've been developing this theory for years and years. Here I am, a member of the public. Convince me that what you're proposing is going to change my life.

Otherwise, I'm simply not interested, and if you can't intrigue a layman, I doubt you're going to win over any experts.
 
Since the traditional mathematicians here are using only verbal_symbolic brain skills, that can't understand that a set (the outer "{" "}") can't be a member of a given set.

In that case they can't comprehend the following theorem:
Being a set is different than being a member of a given set.

Moreover, they can't distinguish between a set, which is a collection of distinct objects, and a multiset, which is not a collection of distinct objects (the same object appears more than once as a member of a multiset).

These two inabilities are enough in order to ignore the rest of the traditional mathematicians' arguments, in this case, but look at the rest of their argument, which forces their enumerable infinity even if no mapping between the members of at least two set is involved in this theorem.

As for the universal set, since being a set is different than being a member of a given set, then no collection of members of a given set is extensible into the level of a given set, or in other words, no collection of members is complete with respect to the level of being a set, and the notion of strict transfinite cardinality is logically false.

Once again the traditional mathematicians here demonstrate how their conventions block their reasoning and do not allow them to get Cantor's Diagonalization in a non-traditional light.
 
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doronshadmi said:
Since the traditional mathematicians here are using only verbal_symbolic brain skills, that can't understand that a set (the outer "{" "}") can't be a member of a given set.
Click to expand...

You're confused again doronshadmi. The {} are not members of a set (generally speaking).

Look at the English language and its grammar rules. Unless you're e.e. cummings, a typical sentence starts with a capital letter and ends with a punctuation mark. The capital letter and the punctuation mark make up the sentence. The opposite is true with mathematics and how the set is written. A { starts the set, and a } ends the set. { and } are not parts of the set.

Go over to Wikipedia and look at the definition of Set. Look for "Describing sets". It doesn't say that the curly brackets are members of the set, or that they are the set.
 
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PiedPiper said:
Doron,

People (including myself) have asked you multiple times for proof that your "organic mathematics" *does* anything meaningful. I'm going to take it a step further:

What, in the context of myself not being a mathematician, can your theory do for me? How will it make my life easier? How will it make my life better? I ask this because in some of your scribd documents you warn vaguely about the destruction of our way of life etc if organic mathematics is not adopted. Don't make me search for the quote, I have no desire to wade through that all over again.

If something is as profound as you say it is, tell me why I should care. Don't use a single variable, don't use a single mathematical equation or concept above middle school level. It's a belief of mine that if you truly understand a subject and it's truly applicable to someones life, that you should be able to explain it at a very low level and the subject should immediately grasp how this is going to change their life. I do it all the time in my field, boiling down extremely complicated chemical phenomena into simple, easy to understand talking points that convince endusers as well as investors.

So here's your chance. You've been fencing with mathematicians for over 40 pages in this thread alone. By your admission you've been developing this theory for years and years. Here I am, a member of the public. Convince me that what you're proposing is going to change my life.

Otherwise, I'm simply not interested, and if you can't intrigue a layman, I doubt you're going to win over any experts.
Click to expand...
You are not a passive factor in what I call The Organic Realm.

It means that you are a meaningful organ of that realm, which is aware of his responsibility to be an active participator of the development of this realm, where development is any harmonious AND consistent expression with the entire expressions of that realm.

Development needs a room in order to be expressed harmonically AND consistently, and this room is exactly the non-entropic conditions that are derived form the irreducibility of Membership into NOthing (that has no predecessor) AND the non-extensibility of Membership into YESthing (that has no successor).

In simpler words, verbal_symbolic AND visual_spatial brain skills are complement each other into a one unified formal reasoning, in order to provide the foundations of the unification among Ethical reasoning (in terms of evolutionary scale) AND Logical reasoning.

This unification can be done in each brain of self-aware creatures like us, where the survival of self-aware creatures is possible if it is developed into Unity-awareness.

The following verbal_symbolic AND visual_spatial expression demonstrates it:

Let's use a cross-section of Riemann sphere through its 0 and ∞ poles.

The concept of Set is closed under the polychotomy of YESthing and NOthing.

That is among Polychotomy is thing (known also as Unity), as follows:

6840987626_c9c426828a_z.jpg


NOthing is weaker than any tool that is used to measure it.

YESthing is stronger than any tool that is used to measure it.

Unity (thing) is among NO,SOME,EVERY,YES Ploychotomy.


I'll say it again and again as long as I live:

In my opinion, the ability to manipulate environments is in direct proportionality with the complexity of the manipulator (where Complexity is not a synonym for Complicated, exactly as Simplicity is not a synonym for Triviality). In order to not be break apart, Complexity must be rooted in Simplicity, such that the balance of the considered manipulator is kept during manipulations. If creatures like us have the power to build today atomic and hydrogen bombs, and tomorrow anti-matter bombs, I think that it is important to develop the tuning between Simplicity and Complexity in order to survive these powers.

As I get it, this simplicity is actually the non-subjective aspect of one's awareness, which enables the subjective aspect at the level of thoughts to be consistent with the subjective aspect of other creatures like us. This consistency may be expressed by the ability to use Ethics (in terms of evolutionary scale that is not restricted into any particular school of thought, religion, culture or civilization) AND Logical\Technological skills, as organs of a one balanced framework, and during the practical interaction among the subjective and the non-subjective, Unity-awareness becomes concrete in daily life. The following diagram is an analogy of Unity-awareness in terms of 1-dimensional space, such that being curved (represents the subjective and complex aspects of a given realm) or straight (represents the objective and simple aspect of that realm) is not known in terms of Dichotomy (where dichotomy is a particular case of Polychotomy):

5721561558_c5b78c3152_b.jpg


According to this interpretation, a given realm is actually consistent, if Unity-awareness becomes concrete in daily life, and maybe the mathematical science is actually fulfilled, if it is used to develop Unity-awareness.

If you wish to get more details, you are invited to look at my latest articles on this subject in http://www.scribd.com/doc/97823738/Unity-Awarness and http://www.scribd.com/doc/98276640/Umes .

PiedPiper said:
Otherwise, I'm simply not interested, and if you can't intrigue a layman, I doubt you're going to win over any experts.
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In my opinion, experts in mathematics (as it is understood and used for the past 4000 years) are probably that last persons that are able to get Organic Mathematics.
 
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Little 10 Toes said:
{ and } are not parts of the set.
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the outer "{" and "}" is exactly the notation of being a set (whether it is empty, or not).

As long as you are using only your verbal_symbolic brain skills (and this is exactly what you are doing, in this case) you can't get that.
 
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