Deeper than primes - Continuation

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Little 10 Toes said:
No it's not. It's a set. You have just declared it a set.
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It is indeed a set, which one of its members is "the set of all ideas".

Since I show in http://www.scribd.com/doron_shadmi/d/95690481-UMES (pages 6,7) that no collection of members is equivalent to the level of a set, then no collection of members is complete w.r.t the level of a set.

Btw, for traditional mathematicians any given day is not the day to get http://www.scribd.com/doron_shadmi/d/95690481-UMES.


Prof. Louis H. Kauffman ( http://en.wikipedia.org/wiki/Louis_Kauffman ) is an a example of an open minded mathematician ( http://www.youtube.com/watch?v=KkYcFaldQ4g ).
 
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Let's research the following statement:

"Without a loss of generality, the given example ( as seen in http://www.internationalskeptics.com/forums/showpost.php?p=8375863&postcount=1557 ) is a visual_spatial proof that the sum of partial observations is not the same as the whole observation."

It has to be stressed that no amount of partial observations (such that each observation can't get the reflexivity of the 1-dimesional element at the level of 3-dimensional space) has the power of the continuum of the whole observation, and the following picture demonstrates that the whole observation (which has the power of the continuum) is not the sum of any amount of partial observations (which do not have the power of the continuum):

7381415562_770125d33a.jpg

The attempt of traditional mathematicians to define the whole in terms of collection of parts, is derived from the invalid verbal_symbolic-only reasoning of hard reductionism.

http://www.internationalskeptics.com/forums/showpost.php?p=8375911&postcount=1558 is an automatic reaction of hard reductionist.
 
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doronshadmi said:
The statement "The set of all ideas" is an idea.

In naive set theory one does not distinguish between the level of a given set and the level of the member of a given set.

Since Organic Mathematics distinguishes between these levels ( http://www.scribd.com/doron_shadmi/d/95690481-UMES page 7 ), it avoids the problems of naive set theory.
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Let's review the foundation axioms for Doronetic set theory. The following is the complete list of axioms provided by Doron:
Doron as his complete list of axioms said:
.
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Now, given those axioms, would anyone care to show how Doronetic set theory meets the claims made by Doron?
 
zooterkin said:
Only in the same way they "do not get" timecube.
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zooterkin your replies are still no more than an automatic reaction of hard reductionist, about the considered subject.

You are invited to show in details how timecube solve, for example, Russell's Paradox, in order to support your claim that timecube and http://www.scribd.com/doc/97823738/Unity-Awarness are not understood by traditional mathematicians "in the same way".

Some hint: you have no chance to say any valuable thing about http://www.scribd.com/doc/97823738/Unity-Awarness by using your hard reductionist verbal_symbolic-only reasoning ( as explained in details in http://www.internationalskeptics.com/forums/showpost.php?p=8376969&postcount=1563 ).
 
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doronshadmi said:
zooterkin your replies are still no more than an automatic reaction of hard reductionist, about the considered subject.
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No, zooterkin's replies smack of reality.

You are invited to show in details how timecube solve, for example, Russell's Paradox, in order to support your claim that timecube and http://www.scribd.com/doc/97823738/Unity-Awarness are not understood by traditional mathematicians "in the same way".
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You might want to re-read zooterkin's post for comprehension and then maybe read some of the timecube material. You seemed to have completely missed his point.
 
Traditional Mathematicians' realm is based on the lack of self awareness of their mathematical work, for example:

On one hand, they define, for example, a universe called "Natural numbers", such that there is nothing between, for example, 2 and 3.

On the other hand, they define, for example, a universe called "Real numbers", such that there is something between, for example, 2 and 3.

It is easily understood that both definitions are no more than subjective manipulations of their awareness, which are resulted by inconsistent observation of what's between 2 and 3.

Furthermore, they claim that their observations are objective reports of a realm that is independent of their observations.
 
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doronshadmi said:
Traditional Mathematicians' realm is based on the lack of self awareness of their mathematical work, for example:

From one hand, they define, for example a universe called "Natural numbers", such that there is nothing between, for example, 2 and 3.

On the other hand, they define, for example a universe called "Real numbers", such that there is something between 2 and 3.

It is easily understood that both definitions are no more than subjective manipulations of their awareness, which are resulted by inconsistent observation of what's between 2 and 3.

Furthermore, they claim that their observations are objective reports of a realm that is independent of their observations.
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So much straw; so little reality.

Is there a 2.5 letter word for nonsense?
 
Is there any chance that a straw man is aware of some realm?

Is there any chance that a traditional mathematician has self awareness?
 
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As can be seen a traditional mathematician does not have self awareness, as a fundamental principle of his reasoning.

After all, what can we ask from minds that get a set and a member of a given set at the same level?

Is there any chance that a creature that is not aware of itself is responsible for the results of its expressions, whether they are abstract or not?
 
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doronshadmi said:
As can be seen a traditional mathematician does not have self awareness, as a fundamental principle of his reasoning.

After all, what can we ask from minds that get a set and a member of a given set at the same level?

Is there any chance that a creature that is not aware of itself is responsible for the results of its expressions, whether they are abstract or not?
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Doron, it is well established you have trouble expressing complete thoughts, your adventures with gibberish are classic, and your demonstrated powers of reasoning would fall short for what is required in elementary school (and if needed I can cite examples of all of these), but, seriously, are you really so morally bankrupt that you must resort to bare-faced lying in an attempt to bolster you position?
 
Once more it is demonstrated that traditional mathematicians derived into contradiction if they refer to their selves.

So, self awareness as a factor of their work, is essentially forbidden.

In other words, natural responsibility is not a factor of their work, and it is easily understood how dangerous are the results of a creature that is not aware of the results of its expressions, both for himself AND the surround environment.
 
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Once again, the attempt of traditional mathematicians to define the whole in terms of collection of parts, is derived from the non-satisfactory verbal_symbolic-only reasoning of hard reductionism, where observation (in therm of self awareness) is not a factor of that reasoning.

As I get it, observation in therm of self-awareness is essential for natural responsibility, where natural responsibility is expressed as a consistent (harmonious) flourishing linkage among self-aware creatures AND the surround environment.

According to this insight, consistent (harmonious) reasoning is at least the linkage among Ethical reasoning AND Logical reasoning.

In my opinion, the current mathematical science has to be developed into the science of the linkage among Ethical reasoning AND Logical reasoning, if we wish to survive further manipulations of nature's forces.

If you ask me, we have lost the privilege to ignore our responsibility of the results of our expressions, and only Logical reasoning does not provide anymore the needed awareness for self responsibility of the results of our expressions.
 
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A quote taken from Louis H. Kauffman's paper Reflexivity and Eigenform: The Shape of Process ( http://www.gwu.edu/~rpsol/preconf/wmsci/kaufman2.pdf ):
In this paper we have covered a number of mathematical structures related to the concept of reflexivity. We have defined the notion of a reflexive domain D as a domain where the elements of that domain and the mappings of the domain to itself are in 1–1correspondence.

In such a context, every object is inherently a process, and the structure of the domain as a whole comes from the relationships whose exploration constitutes the domain. There is no place to hide in a reflexive domain, no fundamental particle, no irreducible object or building block. Any given entity acquires its properties through its relationships with everything else. The sense of such a domain is not at all like the set theoretic notion of collections or unrelated things, or things related by an identifiable property. It is more like a conversation or an improvisation, held up and moving in its own momentum, creating and lifting sound and meaning in the process of its own exchange. Conversations create spaces and events, and these events create further conversations. The worlds appearing from reflexivity are worlds nevertheless, with those properties of partial longevity, emergence of patterns, and emergence of laws that we have come to associate with seemingly objective reality.
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Prof. Louis H. Kauffman has an open mind (unlike traditional mathematicians).
 
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doronshadmi said:
A quote taken from Louis H. Kauffman's paper Reflexivity and Eigenform: The Shape of Process ( http://www.gwu.edu/~rpsol/preconf/wmsci/kaufman2.pdf ):


Prof. Louis H. Kauffman has an open mind (unlike traditional mathematicians).
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Oh, look! Doron googled the word, distinction. Will he able to intelligently discuss what he found, or will it be just another drive-by where Doron thinks he knows what this paper must mean, but can't present that in any way that actually agrees with what was written?
 
jsfisher said:
Oh, look! Doron googled the word, distinction. Will he able to intelligently discuss what he found, or will it be just another drive-by where Doron thinks he knows what this paper must mean, but can't present that in any way that actually agrees with what was written?
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Oh, Sir! Sir! Please Sir! I know! Pick me!
 
Prof. Louis H. Kauffman uses the expression Ω = {Ω} and we can hear how traditional mathematicians jump and say: "use new notations for your non-traditional sets, if you want us to communicate with you".

Traditional mathematicians please look what Prof. Louis H. Kauffman does to standard notations in http://homepages.math.uic.edu/~kauffman/KnotLogic.pdf , for example, at pages 34 or 9.

It is just blasphemy, isn't it traditional mathematicians?
 
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One wonders if doron is going to be honest enough to share with us the replies he will get from his new hero as I am positive he has already started bomarding him with his ground breaking revelations.
 
Unlike Organic Mathematics' reasoning of sets and members ( as shown in http://www.scribd.com/doc/98276640/Umes ), Knot set theory and ZF(C) set theory agree that there is no difference between being a set and being a member of a given set.

According to Knot set theory, being a member is defined as a knot above knot, whether the knot is the same knot, or not.

According to Knot set theory, A = {A} means that knot A is above itself.

Do we have to change the notations in order the avoid confusion with ZF(C) set theory?

Unlike traditional mathematicians (which their notions are closed under notations) I claim that notations are closed under notions, and in this case there is no problem to use the same notation with a different notion.

Organic Mathematics and Knot set theory agree that notations are closed under notions.

Yet Organic Mathematics' reasoning of sets and members ( as shown in http://www.scribd.com/doc/98276640/Umes ) and Knot set theory reasoning of sets and members (as shown http://homepages.math.uic.edu/~kauffman/KnotLogic.pdf , for example, in pages 34 or 9) do not agree with each other, but because their notations are closed under notions, there can be a fruitful discussion between the two theories.
 
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sympathic said:
One wonders if doron is going to be honest enough to share with us the replies he will get from his new hero as I am positive he has already started bomarding him with his ground breaking revelations.
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sympathic, be honest enough to admit that your notions are closed under traditionally agreed notations.
 
So, let's recap.

Doron, by way of his superior google fu, finds himself yet another Mathematics hero. Unlike his previous discoveries, though, this hero is not a crank; he is a perfectly rational mathematician. Moreover, this traditional mathematician has a comprehensible writing style and a skill for complementing his prose with carefully developed notation.

This is, of course, in sharp contrast to Doron's own presentation style of lexical gibberish complemented with symbolic gibberish to express incomplete and contradictory ideas, but I digest. Back to Dr. Kauffman.

Doron exploits his unparalleled skills for misunderstanding and misrepresenting just about anything in Mathematics to, well, misunderstand and misrepresent Kauffman's writings.

Well, done.
 
doronshadmi said:
My view of Knot set theory is shown in http://www.scribd.com/doc/98276640/Umes pages 17,18 .
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Let's start there, then. The first paragraph is a strawman continuing from the confusion on page 16, so we will skip that. You next write:

scribd doron said:
According to Knot set theory (http://homepages.math.uic.edu/~kauffman/KnotLogic.pdf) being a member is defined as a knot above knot, whether the knot is the same knot, or not.
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We will ignore for now the wholesale creation of a whole new branch of mathematical pursuit. Instead, we can focus on being a member is defined as a knot above a knot.

Please point to where Kauffman provides that definition in the cited PDF, then this discussion can continue.
 
doronshadmi said:
Prof. Louis H. Kauffman uses the expression Ω = {Ω} and we can hear how traditional mathematicians jump and say: "use new notations for your non-traditional sets, if you want us to communicate with you".

Traditional mathematicians please look what Prof. Louis H. Kauffman does to standard notations in http://homepages.math.uic.edu/~kauffman/KnotLogic.pdf , for example, at pages 34 or 9.

It is just blasphemy, isn't it traditional mathematicians?
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Nope, it's not blasphemy. The expression "Ω = {Ω}" can be stated using standard terminology, "The set named Ω is equal to an element named Ω."
 
Little 10 Toes said:
Nope, it's not blasphemy. The expression "Ω = {Ω}" can be stated using standard terminology, "The set named Ω is equal to an element named Ω."
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Actually, in context, Kauffman was being creative relating knot interrelationships to a self-containing set concept. Knots can be linked to themselves (A={A}), and knots can be inseparably linked to other knots (A={B}, B={A}). He did a reasonable good job of developing those interrelationships at a slow, digestible pace. His notation complemented and reinforced his ideas rather being a cryptic array of symbols pretending to substitute for a concept never explained. He may have gotten carried away once where he overworked the meaning assigned to a variable, X, but it was just a minor bump unlike the death-defying leaps of illogic often presented by cranks.

It is also clear Kauffman enjoys his chosen field of study.
 
1) The traditional mathematicians in this thread failed to find the mistake that I put in http://www.internationalskeptics.com/forums/showpost.php?p=8413600&postcount=1591 and in http://www.scribd.com/doc/98276640/Umes in the second paragraph of page 18, exactly because they do not use verbal_symbolic AND visual_spatial reasoning (and because I am not one of their accepted guys, and in this case they simply ignore what I express) .

Here is the right one (the mistake is using the term above instead of below, in order to define a member by Knot set theory):

According to Knot set theory ( http://homepages.math.uic.edu/~kauffman/KnotLogic.pdf ) being a member is defined as a knot below knot, whether the knot is the same knot, or not. Furthermore, being completely below a given knot, is resulted by null set. Since observation is a significant factor of Knot set theory, it must be stressed that knot being below knot is done by using observation from higher (or wider) dimensional space. In that case the higher dimensional space is equivalent to a given set (notated by the outer "{" "}") where the knots below are equivalent to members, which are always below a given set (YESthing) and above NOthing (please see page 3). In this case reflexivity is actually satisfied in terms of self-awareness only if there is a difference between sets and members of sets.
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2) As can be seen in page 7 of http://homepages.math.uic.edu/~kauffman/KnotLogic.pdf, Prof. Kauffman actually defines and uses infinite self-reference recursion:
Let FIST (First Infinite Sets) denote the class (not necessarily finite) disjoint collections of rectangles in the plane such that each collection S has a single outermost rectangle, and the collection of rectangles inside that outmost rectangle is a disjoint union of elements of FIST (These are the members of S).
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Let's expose the hypocrisy of the traditional mathematicians in this thread, about infinite self-recursion:

In http://www.internationalskeptics.com/forums/showpost.php?p=8258994&postcount=1550 I use self-recursion, which avoids Russell's paradox, because a set and a member of a given set are not at the same level.

The traditional mathematicians completely ignore this solution, by taking what I wrote and force it under Naive set theory, as seen in post #1554.

In other words, the traditional mathematicians are closed under their own traditional view (and their closed list of their accepted guys) of the considered subject, when they write:

"Yes, and this is way the naive set theory is, well, naive. It isn't suitable for any formal result that admits this sort of self-reference.

Why do you insist on deriving Doronetics from something known not to work?"

They also completely ignore post #1555, exactly because this post is not closed under their traditional-only reasoning, and because it was not written by one of their accepted guys.

Now, what the traditional mathematicians write about Prof. Kauffman's FIST?

Answer: Nothing.

Furthermore, here is their reply about Prof. Kauffman's work as done in http://homepages.math.uic.edu/~kauffman/KnotLogic.pdf :

"Actually, in context, Kauffman was being creative relating knot interrelationships to a self-containing set concept. Knots can be linked to themselves (A={A})"

So now infinite self-referential recursion is creative just because it is done by Prof. Kauffman, which is considered by the traditional mathematicians as one of their guys.

Moreover, Prof. Kauffman uses already agreed notations like "{" "}" in a non-standard way, but since he is one of the accepted guys he is creative.

If one of the non-accepted guys will do such a thing, he will be marked by traditional mathematicians as a crank.

If a non-accepted guy makes a mistake or does not properly defines his notions, then this is the "end of the story" for him from now on.

If an accepted guy makes a mistake or does not properly defines his notions, then "He may have gotten carried away once where he overworked the meaning assigned to a variable, X, but it was just a minor bump ..."

Say no more.
 
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