Can you remain silent, Doron, when confronted by noise all around you? So far you have not demonstrated that capability. Nor have you demonstrated the fundamental intents of Transcendental Meditation which is to free yourself (at least temporally and as much as possible) from your own thoughts and perceptions. Instead you take from your perceived experience in Transcendental Meditation your thoughts on the basis of, well, thought. Which only indicates that you weren’t doing it right and that TM is something else that you do not understand, but simply choose to contort to your own perceptions and thoughts. So in your thinking that you are not thinking or your perceptions while believing you're lacking perception, what do you ascribe them to if not yourself?
L10T asked you this very question, yet at least on that subject you have remained silent.
I generalize it to "a"=Element "is"=Relation and any researchable mathematical universe is at least Relation Element Interaction (REI) (where Relation is non-local w.r.t Element, and Element is local w.r.t Relation, exactly as any member is local w.r.t its set, and the set is non-local w.r.t its member).
Great. Now, what do you mean by "distinction is a first order property"?
Distiction is the state that is based on REI and deteminates the identity of a given Element and also the size of a cardinal, where cardinality, according OM, is the magnitude of the existence of a thing).
Well again, jsfisher, as Doron tells us it is based on his perceptions of thought during his transcendental meditations, when he is supposed to be freeing himself of his perceptions and thoughts, even about thought. He simply asserts that his perceptions and thoughts about thought are without basis or merit even just within his own notions, perceptions and thoughts.
Please do not paste identical or near identical versions of the same post, especially very long posts. Instead, link the previous post and indicated corrections.
Replying to this modbox in thread will be off topic Posted By: Tricky
Well I see that bit about “let there be silence” didn’t last too long. Hey Doron, how about simply referencing what you’ve changed, where you changed it and why. Do you really expect people to wade through your regurgitated word salad every time you change a crouton or two? I know tomorrow is Easter, but is this your idea of an Easter egg hunt, ‘find the changes in Doron’s notions that lay an egg with almost every statement’.
Organic Mathematics (OM) is based on the concept of Distinction as a first-order property of any research.
At the first stage two extreme states that are not researchable on their own are defined, which are: Total Emptiness and Total fullness.
The cardinality of OM measures the magnitude of the abstract existence of the researchable, and indeed by OM Total Emptiness has cardinal 0 and Total Fullness has cardinal ∞ . Cardinal 0 has no predecessor, Cardinal ∞ has no successor and no one of them is researchable on its own.
Please try to research Total Emptiness or Total Fullness, and you will get by yourself that these extremes are not researchable on their own.
According OM, the cardinal of any researchable thing is at least stronger than 0 and at most weaker than ∞.
The researchable domain enables the existence of the concept of Collection, where Collection is the result of the interaction between a non-local property known as Relation and a local property known as Element.
Relation is a weaker (and therefore researchable) version of Fullness, and it is researched as the property that can be found between an Element to itself, or between an Element to another Element.
Element is a stronger version (and therefore researchable) of Emptiness, and it appears as the property that saves the identity of the researched.
For example:
A=A means that Element A's identity is saved by self-reference of Relation = from A to itself.
A≠B means that Element A is distinguished from Element B (and vice versa) by Relation ≠.
If the concept of Collection is understood as the result of the interaction between the non-local with the local, it is possible to define superposition of Element's identities, as a first-order property of the concept of Collection.
In that case it is realized that the concept of Set (which is used as a fundamental concept of many mathematical branches) is nothing but the particular case of a collection that has no superposition of identities among its Elements.
From a more general viewpoint of the concept of Collection, if Distinction is used as a first-order property of it, then both superposition of Elements' identities or clear distinction of Elements' identities are some particular cases of Distinction.
These notions have an influence on axiomatic systems like ZF or Peano axiomatic system, if in addition to the standard analytic serial (step-by-step) research; they are researched also by a parallel thinking style, which enables to research its subjects at-once (which is not a step-by-step thinking style).
It means that OM suggests a paradigm-shift of the way of how we research fundamental formal concepts like Logics, Set, Number, Relation, Element, Non-finite, Cardinal, Limit, Completeness, and more …
Slide 2 demonstrates perception's least states represented by Bulge within Socket, Socket within Bulge or none of them.
Slide 3 demonstrates perception's least states represented by Emptiness, Fullness or none of them.
Slide 4 demonstrates Relation and Element as the building-blocks of any formal predicate, where Relation is non-locality that refers form an Element to itself, where an Element is locality.
Slide 5 demonstrates Relation\Element Interactions as the basis of Function(Relation)\Parameters(Elements) or Predicate(Relation)\Variables(Elements). By Relation\Element Interaction (REI) we get a unified first-order state for any mathematical research.
Slide 6 demonstrates researchability as = Relation from an Element to itself, or as ≠ Relation from an Element to another Element.
Slide 7 demonstrates REI as the basis of mutual independency, where total independency is the weak limit (that has no predecessor) and total mutuality is the strong limit (that has nor successor) of the researchable space. The magnitude of the existence of the researchable space is the result of REI and its cardinality is stronger than card 0 and weaker than card ∞.
Slide 8 demonstrates REI in terms of the magnitude of the existence of Locality and Non-locality within the researchable mathematical universe.
Slide 9 demonstrated the mathematical universe that enables the existence of the concept of Collection, which is stronger that total isolation (Locality on its own) and weaker that total connectivity (Non-locality on its own).
Slide 10 demonstrates the difference between local element (belongs XOR does not belong to a given domain) and non-local element (belongs AND does not belong to a given domain).
Slide 11 demonstrates different conclusions that depend on the observation order between local and non-local elements. The observations' conclusions are influenced by the property of the observer, therefore it is called relative observation.
Slide 12 demonstrates different conclusions about X and Y elements that are not influenced by the order of the observation and not by the properties of the observed, because the observation is done from a viewpoint (W) that is external to X or Y, and therefore it is called an absolute observation.
Slide 13 demonstrates the limitation of the serial-only thinking style that does not distinguish between local and non-local element and as a result it concludes contradictions about the research of a non-local element.
Slide 14 demonstrates how a collection is both non-local and local case of the researchable mathematical universe, where this mathematical universe is measured by the symmetrical degrees that exist between superposition of identities or clear identities of the researched elements. Distinction is used as a first-order property of the researchable mathematical universe.
Slide 15 demonstrates the limitation of the serial-only thinking style, which limits itself to the particular case of clear Distinction as the first-order property of the researched.
Slide 16 demonstrates the Organic Numbers that cannot be used both as cardinals and ordinals, unless we are using only the particular case of clear distinction. Each ON is simultaneously Local and Non-local form of the entire system.
Slide 17 defines Redundancy and Uncertainty.
Slide 18 demonstrates the Organic Number as the researchable space between Redundancy and Uncertainty.
Slide 19 represents the Organic Numbers by the particular case of order according clear distinction under finite cardinals (the framed ON's are simultaneously local and non-local case of the entire system).
Slide 20 demonstrates how ONs can be used to extend known series like Fibonacci series.
Slide 21 demonstrates an extension of the Partition Function (this extension is still the particular case of clear distinctions between different distinct states, which are nested under finite cardinals).
Slide 22 demonstrates an extension of the Partition Function (this extension is still the particular case of clear distinctions between different distinct states, which are nested under finite cardinals) of cardinal 5.
Slide 23 demonstrates the complement connection between Multiplication (an operation between elements that are in superposition with each other) and Addition (an operation between elements that are not in superposition with each other).
Slide 24 defines the Real-line as a non-local urelement, which enables the discovery\invention of the non-local numbers.
Slide 25 demonstrates non-local numbers that are based on the base value method, which are understood by the standard paradigm as numerals because the real-line is not a non-local urelement by the standard paradigm.
Slide 26 demonstrates possible numerical extensions based on the base value method, if the real-line is a non-local urelement.
Slide 27 demonstrates Organic Fraction, which is the outcome of different distinctions of different finite cardinals upon different scale levels.
Slide 28 demonstrates the incompleteness of a non-finite collection if it is compared to a non-local element. Cantor's second diagonal is actually a proof of the incompleteness of any collection if it is compared to the non-local real-line. This is not a geometrical comparison. This is a comparison that is based on combining serial and parallel observations of the mathematical subject. Please pay attention to the fact that no mapping between N and R is researched here. Instead, the comparison is between Collection and non-local urelement (the real-line as a non-local element).
Slide 29 demonstrates a new understanding about arithmetical operations with non-finite collections. The model of Tachyon (a hypothetic particle that its minimal speed is not less than the speed of light) is used here in order to show that operations like Subtraction, Division, Square root etc. do not change the non-finite collection to a finite collection. On the contrary arithmetical operations like Addition, Multiplication, Exponent etc. increase the magnitude of a non-finite collection. This increase is incomplete because no collection has the magnitude of the non-local real-line.
Slide 30 uses the Organic Number form in order to demonstrate that if Distinction is a first-order property then there is always a superposition between the identities of a researched collection, in addition to the uncertainty about its exact magnitude, which is incomplete if compared to the non-local urelement real-line.
Slide 31 stresses the connection thinking styles and mathematical developments under a one unified framework.
I have gone back to the previous versions of this post and replaced them with links to this one. In the future, doronshadmi, please do not repeat identical or nearly identical posts, especially long ones. It is considered "flooding" the forum. If you need to make changes, link the first post and indicate the changes in the new post rather than repeating everything.
Thank you
Tricky
Replying to this modbox in thread will be off topic Posted By: Tricky
So is this you finial finial version or should we wait till tomorrow before we start revamping the entire field of mathematics and research to conform with your notions?
So now we have bulging sockets of perception and a complete Doron connection between multiplication and addition. Just when I though nothing could be missing from your notions (well, I mean other then meaning).
ETA:
So with your new bulging sockets of perception, are you inferring that your ‘OM’ is just an optical illusion?
indeed as that he doesn't want contradiction. He just wants us to "listen" to him. He's proven unable to give meaningful answers to questions anyway, so what's the point in posing more questions?
Oh, and I did report the senseless repetition of his "explanation" of his PPT.
indeed as that he doesn't want contradiction. He just wants us to "listen" to him. He's proven unable to give meaningful answers to questions anyway, so what's the point in posing more questions?
Oh, and I did report the senseless repetition of his "explanation" of his PPT.
Well it certainly made the past posts on the thread and Doron in particular suddenly seem more silent. Now if he can just break his definitive silence with something at least actually salient.
“Ask not for whom the bell tolls; it tolls for thee” . Unfortunately, in this case the bell tolls with a resounding thud.
ETA:
As far as a critique goes, I find it quite telling that said PP presentation simply regurgitates points we have already critiqued without incorporating, well, those critiques or any viable response.
Like any con, when the fish aren't biting one place more to another stream. Though I doubt hell have much luck there especially if he is just reusing the same old worn out bait.
Like any con, when the fish aren't biting one place more to another stream. Though I doubt hell have much luck there especially if he is just reusing the same old worn out bait.
Thus far, Doron has tried to peddle his nonsense on over 50 different internet fora. On most, he has been laughed at hard, on some just not gotten any reaction and banned on 7. The reactions on Talk Rational thus far sound promising.
Let X be a placeholder for any thinkable thing. X can be measured by using Set as a measurement tool, where Cardinal is the measurement unit. For example, the ZF axiom of the Empty Set states that: "There exists set A such that any set (including A) is not a member of A". By OM this axiom is understood as follows: "There exists set A" means that if set A is measured as a member of some set, for example B={A}, then the cardinal of B is at least 1. If we generalize it to "There exists set", then the magnitude of the existence of a Set is at least 1. Following the same reasoning, the magnitude of the existence of Emptiness is 0, where the magnitude of the existence of its opposite, called Fullness, is ∞. In each one of these examples, Set is used to measure the magnitude of the existence of X.
In the case of the Empty set, X is the absence of members. In the case of the Full set, X is stronger than any member. "X is stronger than any member" is what OM calls Relation, known as "Membership" by Set Theory or "Morphisms" by Category Theory.
In both theories Collection is the result of Relation Element Interaction (REI), where the cardinality (the magnitude of the existence) of this result is > 0 and < ∞.
The magnitude of the existence of a set is not determined by its members if these "members" are Emptiness or Fullness. Emptiness or Fullness are not researchable directly, because Emptiness' existence on its own is too weak, and Fullness' existence on its own is too strong. For example, The Empty Set is not itself Emptiness but it is an existing thing that is used to define the Cardinal of Emptiness, where Emptiness' "existence" itself is weaker than any existing thing. Also the Full Set (the opposite of the Empty set) is not itself Fullness but it is an existing thing that is used to define the Cardinal of Fullness, where Fullness' "existence" itself is stronger than any existing thing.
In that case the concept of Set has a magnitude of existence that is stronger than 0 (the magnitude of the "existence" of Emptiness that can be defined only indirectly by using an existing and researchable thing like Set) and weaker than ∞ (the magnitude of the "existence" of Fullness that can be defined only indirectly by using an existing and researchable thing like Set). By getting the notion of the extreme non-researchable states (Emptiness or Fullness on their own) one defines the general concept of Collection, where its magnitude of existence is stronger than Emptiness on its own and weaker than Fullness on its own.
If we generalize Sets or Categories by these notions, then Memberships (Set) or Morphisms (Category) magnitude of existence are weaker than Fullness on its own and stronger than Members (Set) or Objects, where Members (Set) or Objects (Category) magnitude of existence are stronger than Emptiness on its own and weaker than Memberships (Set) or Morphisms (Category). If Memberships or Morphisms are Relation and Members or Objects are Element, then the magnitude of existence of a non-empty collection is determined by the amount of its Elements, gathered by Relation.
In order to distinguish between the researchable and the non-researchable, let us symbolize it as follows:
Emptiness on its own is represented by the background of this page.
Fullness on its own is represented by the opposite background of this page.
Relation is represented as _
Element is represented as •
Interaction (Bridging) between Relation and Element is represented as |
OM's development is possible because we determine the limits of the researchable by using the weak limit (Emptiness) and the strong limit (Fullness). Cantor distinguished three levels of existences:
1) In the mind of God (the Intellectus Divinum)
2) In the mind of man (in abstracto)
3) In the physical universe (in concreto)
By using Fullness as "that has no successor" we show that Cantor's in abstracto Transfinite system is not an actual infinity. We also show how Distinction is a first-order property of any collection. These developments are based on a cognitive approach of the mathematical science. In "On the Reality of the Continuum" [1] (page 124) we find this sentence:
"From the realist standpoint, numbers and other real things do not need admitting or legitimating by humans to come into existence."
From the idealist standpoint, numbers and other real things do need admitting or legitimating by humans to come into existence. In both cases the term "real thing" has to be understood. According to the realist if "real things" are "real" iff they are totally independent of each other, then no collection is a "real thing" (total independency does not able things to be gathered).
According to the idealist if "real things" are "real" iff they are totally dependent of each other, then no collection is a "real thing" (total dependency does not able things to be identified). No collection exists in terms of total dependency (total connectivity) or total independency (total isolation). Since totalities are not researchable on their own, then any research cannot avoid the existence of collections, where collections are the only researchable "real things". Actually we find that a researchable realm is both ideal (has relations) and real (has elements).
We have to notice that there is no symmetry in using concepts like "Realist standpoint" in order to understand "real things" because if the requested result is "real things" then we actually give a privilege to the Realist standpoint over the Idealist standpoint about the requested "real thing". This asymmetry can be avoided by changing the requested results to "researchable things" instead of "real things". In that case the concept of Collection is researchable exactly because it is not totally real and not totally ideal.
Here is the last part of the quote from [1]:
"Furthermore, real objects are always legitimate objects of study in the sciences, even if they are not fully understood or known."
We agree with this quote because "real objects" are valuable for science iff they are researchable, or in other words, they are both real and ideal.
For further clarification of my work with Moshe Klein on this subject, please see the attached links:
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