Deeper than primes

[doronshadmi]

Yes, your post is a collection of distinct objects called "words," but I don't understand how the set Post can be closed under collection of those words. The terminology "closed under" applies to the operations that the members of a set are subjected to. For example, R is closed strictly under addition and multiplication. You should explain what kind of operation the "collection of distinct object" is, otherwise you could be charged with forceful sodomy performed on juveniles. (The set theory is a relatively young field of mathematics.)

"Closed under" holds for any subject that is researched by using partial skills.

By using only verbal_symbolic skills in order to get the Mathematical science, one is actually closed under the limitations of partial abilities of one's skills.

Set theory in its classical form, is the result of using only verbal_symbolic skills.

By being closed under this limitation one actually can't understand the implications of non-homeomorphism among different mathematical/physical spaces.

As a result one can't comprehend Non-locality and Locality, Actual and potential infinity, the power of the continuum of a given "host" space w.r.t collections of "hosted" spaces on it, Cross-contexts and Context-dependent reasoning, and many more interesting facts that are available if verbal_symbolic AND visual_spatial skills are used as a one comprehensive framework.

Please look at the following article http://arxiv.org/PS_cache/physics/pdf/0605/0605061v152.pdf which uses visual_spatial skills by translating them into verbal_symbolic skills.

By doing that verbal_symbolic AND visual_spatial skills still do not fulfill the ability to be used as a one comprehensive framework.

But by using verbal_symbolic AND visual_spatial skills, such that (for example) __ is 1-dim space and . is 0-dim space, it is obvious that . is the smallest possible space and no __ space can be . (and vise versa).

As a result __ is no more than smaller space w.r.t to . smallest space, such that given two smallest spaces .. there is always __ between them, which is no more then smaller space w.r.t them.

Furthermore, __ is located AND not located w.r.t each one of the two given smallest spaces .. exactly because it is no more than smaller space w.r.t to them.

On the contrary, a given . space is located XOR not located w.r.t to any given space that is not itself.

So by using verbal_symbolic AND visual_spatial skills one understands Non-locality and Locality.

 

[epix]

"Closed under" holds for any subject that is researched by using partial skills.

By using only verbal_symbolic skills in order to get the Mathematical science, one is actually closed under the limitations of partial abilities of one's skills.

Set theory in its classical form, is the result of using only verbal_symbolic skills.

By being closed under this limitation one actually can't understand the implications of non-homeomorphism among different mathematical/physical spaces.

You seem to excel on the theme of the set closures, which is peculiar in the view of my statement

For example, R is closed strictly under addition and multiplication.

which you left floating on the surface of reason without raising any objection. Isn't it true that the example applies to N rather than to R?

Theories are usually rendered formally in the symbolic language, but they are not created that way. Some honest folks like Albert Einstein provided enough clue to what enters the mind. Actually Cantor believed that it was God who disclosed to him the "simple and beautiful" proofs. Andrew Wiles of the Last Fermat Theorem fame pretty much described what happened when he hit the dead end. God helps those who help themselves. In other words, you need to try and show willingness before tricks kick in. But there are plenty of ignorant pretenders who lie about the abilities of the human mind -- the mediocre of the flock who are not humble enough . . .

Is there something like the "second brain"?
http://www.lib.uni-bonn.de/PhiMSAMP/GAP6/Talks/Devlin.pdf

You hint that your insights are so profound that only "spatial_visual" skills can unlock the reason behind them. You can keep lying to yourself and continue your gobbledygook. That's not gibberish; the word actually stands for something:

Language that is meaningless or is made unintelligible by excessive use of abstruse technical terms; nonsense.

The visual representation of the set theory is unreliable:

T = {a, o, b}


(frui)T = {a, o, b}


T = {a, o, b}

 

[jsfisher]

In my opinion, any definition is unsatisfied if it is not based on visual_spatial AND verbal_symbolic skills.

Talk about self-serving rubbish.... Since Doron has neither skill, his opinion is baseless.

Ideas can be expressed in words, and ideas can be expressed in images. Often times, words supplemented with images is a very effective presentation. Unfortunately for Doron, he has proven himself incapable of meaningful verbal or visual communication. Instead, he provides two seemingly uncorrelated versions of gibberish then blames everyone else for their lack of comprehension.

Rubbish.

 

[doronshadmi]

You hint that your insights are so profound that only "spatial_visual" skills can unlock the reason behind them.

epix, do you understand the difference between "only "spatial_visual" skills" and verbal_symbolic AND visual_spatial skills?

If your answer is NO, then you are going to my ignore list.

 

[zooterkin]

epix, do you understand the difference between "only "spatial_visual" skills" and verbal_symbolic AND visual_spatial skills?

If your answer is NO, then you are going to my ignore list.

I don't suppose you'd like to define either of those terms? Or would that require the use of interpretive dance?

 

[epix]

epix, do you understand the difference between "only "spatial_visual" skills" and verbal_symbolic AND visual_spatial skills?

If your answer is NO, then you are going to my ignore list.

What makes you think that I don't understand the difference? Can you quote the post or a part of it that gave you the impression that I don't understand the difference?

Before that happens - if ever - I think you should get acquainted with an opinion of a mathematician who not only knows what he is doing but also how he is doing in it. I've already provided the link.

Of particular relevance to my thesis are the mathematicians’ descriptions of the way they arrived at the solutions to problems they had been working on. Time and again, the solution came at a quite unexpected moment, when the person was engaged in some other activity and was not consciously thinking about the problem. Moreover, in that inspirational moment the whole solution suddenly fell into place, as if the pieces of a huge jigsaw puzzle had been dropped onto the floor and miraculously landed as a complete picture. The mathematician “saw” the solution and instinctively knew it was correct.

No language is involved in this process. Indeed, with a problem for which the solution is fairly complex, it might take the mathematician weeks or even months to spell out (in linguistic form) the step-by-step logical argument that constitutes the official solution to the problem — the proof of the result.

Here is a supporting word from Einstein and Hadamard respectively:

Words and language, whether written or spoken, do not seem to play any part in my thought processes. The psychological entities that serve as building blocks for my thought are certain signs or images, more or less clear, that I can reproduce and recombine at will.

I insist that words are totally absent from my mind when I really think . . . even after reading or hearing a question, every word disappears the very moment that I am beginning to think it over.

If you ponder the highlighted and imagine the very abbreviated explanation of topological spaces rendered in the formal language in Wikipedia, then it may take more than a month to set up the environment that leads toward understanding of the issue; and it takes a second to call anyone who peruses the text in order to learn the concept and claims that he now knows a liar.

Now you open your axioms with "C is a set" and then you put a restriction on one clause of the axiom, which prohibits "picking" one member no more than twice. Obviously, the confidence of the reader that you know what you are talking about is gone. Reminded of the problem, you change the definition from "C is a set" to "C stands for Collection" without bothering to specify the type of collection and the operation done on its members. Instead, you call upon those verbal_symbolic and spatial_visual skills to do the job. You offer repeatedly only one "spatial_visual" example, which is counter-intuitive, like any other of your visual supplements. Do you think I would bother to keep examining? I leave it to The Man or jsfisher, and then I read about it. If there is nothing to read about, then it's obvious that your "spatial_visual" argument is some kind of nonsense and my suspicion was correct.

Redo the circles, try again and again until a child understands it, if it's not a nonsense.

 

[doronshadmi]

What makes you think that I don't understand the difference?

Can you quote the post or a part of it that gave you the impression that I don't understand the difference?

Yes.

You hint that your insights are so profound that only "spatial_visual" skills can unlock the reason behind them.

Instead, you call upon those verbal_symbolic and spatial_visual skills to do the job. You offer repeatedly only one "spatial_visual" example, which is counter-intuitive, like any other of your visual supplements.

epix, it is counter-intuitive as long as you do not use verbal_symbolic AND spatial_visual skills as a one comprehensive framework.

By the way "the step-by-step logical argument that constitutes the official solution to the problem — the proof of the result" is an example of using verbal_symbolic_only skills.

This time, please read all of http://www.internationalskeptics.com/forums/showpost.php?p=7637828&postcount=16521 , before you are talking about counter-intuitive.

 

[The Man]

That Ignore List is actually a subset, coz there are no duplicate nicknames in JREF. So if that subset comes under the influence of those two Doron's axioms, then the promised action taken by him can have an unexpected result, like he can even PM you.

If ‘PM’ means Purposely Misrepresent then that's about all he has been doing.

 

[epix]

Yes.



epix, it is counter-intuitive as long as you do not use verbal_symbolic AND spatial_visual skills as a one comprehensive framework.

By the way "the step-by-step logical argument that constitutes the official solution to the problem — the proof of the result" is an example of using verbal_symbolic_only skills.

This time, please read all of http://www.internationalskeptics.com/forums/showpost.php?p=7637828&postcount=16521 , before you are talking about counter-intuitive.

Your verbal descriptions are almost always disconnected from your visual renditions. It only takes a few questions to confirm the suspicion that you are not at the helm of your own thoughts. You know it and that's why you ignore answering them or you perform an evasive maneuver. You are addicted to shuffling and connecting math terms that you read elsewhere and putting them stripped of any meaning on the billboard advertising Doronetics. And for the crimes committed against Plus and Minus, I therefore find you guilty as charged and hereby sentence you to counting to one hundred and backward with no possibility of skipping.

 

[doronshadmi]

Your verbal descriptions are almost always disconnected from your visual renditions. It only takes a few questions to confirm the suspicion that you are not at the helm of your own thoughts. You know it and that's why you ignore answering them or you perform an evasive maneuver.

epix, you still do not use verbal_symbolic AND and visual_spatial skills in order to realize that (for example) all possible line segments can't be smallest as a point, such that given any arbitrary closer points, there is always a line segment between them, which is greater than the points (which are the smallest elements).

This simple fact clearly shows that the power of continuum of 1-dimensional mathematical space is greater than the power of the collection of all 0-dimensional spaces on it.

Your inability to get what I have just wrote is beyond any suspicion, but you can't know that because your reasoning is closed under to power of the collection of all 0-dimensional mathematical spaces on (for example) a given 1-dimasional mathematical space (you wrongly define a given 1-dimensional mathematical space in terms of the 0-dimensional mathematical spaces on it).

Furthermore, you wrongly define the collection of all smallest objects ((known also as points or 0-dimensional mathematical spaces) on (for example) a given 1-dimensional mathematical space) as uncountable, exactly because you are not using also your visual_spatial skills, in order to really get this collection with respect to the power of the continuum of the "host" mathematical space (for example, the 1-dimensional mathematical space).

As a result all you get is the one-to-one correspondence between these smallest elements and their verbal_symbolic interpretations, known as the distinct members of R set.

By using only your verbal_symbolic skills you simply unable to get the 1-dimansiomal mathematical space between the members of R set, which is actually the "host" mathematical space of them that its power of continuum is inaccessible to R set (it is actually inaccessible to ...power(power(power(R)))... ad infinituum).

Because you are using only verbal_symbolic skills you can't actually understand the fact that the outer "{" and "}" symbols are exactly the inaccessibility of any given collection to the power of the continuum of a given "host" mathematical space (where the fact that "{""}" is the notation of the a given "host" mathematical space, is really understood only by using verbal_symbolic AND visual_spatial skills).

By using verbal_symbolic AND and visual_spatial skills it is immediately understood that no collection of "hosted" mathematical spaces has the power of the continuum of the "host" mathematical space.

Again, as long as your mathematical reasoning does not use verbal_symbolic AND and visual_spatial skills as a one comprehensive framework, you simply can't get this post.

 

[jsfisher]

epix, you still do not use verbal_symbolic AND and visual_spatial skills in order to realize that (for example) all possible line segments can't be smallest as a point, such that given any arbitrary closer points, there is always a line segment between them, which is greater than the points (which are the smallest elements).

The gibberish is strong in this one....

This simple fact clearly shows that the power of continuum of 1-dimensional mathematical space is greater than the power of the collection of all 0-dimensional spaces on it.

This would be true if the infinite behaved like the finite. It doesn't, and this isn't.

...<more nonsense>...

 

[doronshadmi]

Anyone that gets things only by verbal_symbolic skills, can't understand the lack of homeomorphism among different mathematical spaces.

Different mathematical spaces are distinct w.r.t each other, such that the greater mathematical spaces are the "host" mathematical spaces of the smaller (and therefore "hosted") mathematical spaces.

Being "hosted" means that the smaller (including the smallest) mathematical spaces are not the building-blocks of the "host" mathematical spaces, or in other words, the "host" mathematical spaces are not made of the "hosted" mathematical spaces.

The smallest mathematical space is 0-dimansional space, which is stronger than emptiness (where emptiness is that has no predecessor), and all the possible infinitely many mathematical spaces that are greater than 0-dimensional mathematical space, are smaller than fullness (where fullness is that has no successor).

Emptiness is the weakest limit of the mathematical science.

Fullness is the strongest limit of the mathematical science.

Collections are the intermediate mathematical universe, which is considered as intermediate if it is inaccessible to these limits.

Unity is absolute symmetry, such that Emptiness,Fullness and the intermediate mathematical universe, are indistinguishable.

 

[jsfisher]

...<self-serving gibberish>...

So, when Doron said he was ignoring several of us, he wasn't being completely honest. I'm shocked, I tell you. Shocked!

 

[epix]

epix, you still do not use verbal_symbolic AND and visual_spatial skills in order to realize that (for example) all possible line segments can't be smallest as a point, such that given any arbitrary closer points, there is always a line segment between them, which is greater than the points (which are the smallest elements).

In my practical applications, I treat points as a dimensionless reference and so your superlatives, like "smallest," are meaningless in that respect. Show me an example, a real computational problem, where in order to solve it, I need to ascribe some dimension to the point so it would be smaller than a line segment whose length is approaching zero.

I can only guess, but it seems to me that you may not be aware of a certain difference. Check out this hardware:
http://www.maniacworld.com/flash-chess.jpg

The stones move around the board according to a set of rules -- you can liken them to axioms. The rules are invariant.

Now check out this hardware:
http://static.howstuffworks.com/gif/poker2.jpg

There are 52 cards in the deck, and, unlike in chess, there are many sets of rules, each set defining a different card game: there are rules (axioms) according to which poker is played, there are rules (axioms) according to which blackjack is played, and so on. But you think that there is only one true card game -- some doron canasta -- and you are trying to invent the rules for it thinking that all other card games are biased to a lesser or greater extent. Every card player knows what "flush" means, but you love to rename the established and come up with your own terms, maybe like "local toilet," and relentlessly try to teach your invention to others -- a card game invention where king of spades is less than king of hearts, but queen of spades beats queen of hearts including all sevens AND eights AND the aces, but not two of diamonds. Your rules (axioms) are too weird and outright illogical for any game apart from howhigh solitaire.

 

[doronshadmi]

In my practical applications, I treat points as a dimensionless reference and so your superlatives, like "smallest," are meaningless in that respect.

0-dimesional mathematical space is not the same as the lack of mathematical dimensional space.

Actually because you are using only verbal_symbolic skills in order to understand what I wrote above, you can't comprehend the difference between 0-dimesional mathematical space and the lack of lack of mathematical dimensional space (called by you "dimensionless").

Once again it is shown that if one does not use verbal_symbolic AND visual_spatial skills as a one comprehensive framework, one actually fails to comprehend the discussed fine subject.

Show me an example, a real computational problem, where in order to solve it, I need to ascribe some dimension to the point so it would be smaller than a line segment whose length is approaching zero.

Once again, 0-dimesional mathematical space is not the same as the lack of dimension, exactly as the cardinality of the empty set (=0) is not the same as Emptiness).

0 is understood by verbal_symbolic skills and Emptiness is understood by visual_spatial skills, and the difference between (for example) 0 cardinality and (for example) Emptiness, is understood only if one uses verbal_symbolic AND visual_spatial skills as a one comprehensive framework.

epix, you still do not do anything in order to get the discussed fine subject by using verbal_symbolic AND visual_spatial skills as a one comprehensive framework.

If you actually use verbal_symbolic AND visual_spatial skills as a one comprehensive framework, then (and only then) you can understand the following:

The smallest mathematical space is 0-dimansional space, which is stronger than emptiness (where emptiness is that has no predecessor), and all the possible infinitely many mathematical spaces that are greater than 0-dimensional mathematical space, are smaller than fullness (where fullness is that has no successor).

Emptiness is the weakest limit of the mathematical science.

Fullness is the strongest limit of the mathematical science.

Collections are the intermediate mathematical universe, which is considered as intermediate if it is inaccessible to these limits.

Unity is absolute symmetry, such that Emptiness,Fullness and the intermediate mathematical universe, are indistinguishable.

I need to ascribe some dimension to the point so it would be smaller than a line segment whose length is approaching zero.

By your own words you ascribed "zero" as the dimensional mathematical space of a point, where no line segment has "zero" mathematical dimensional space (it approaches AND not reaches "zero" mathematical dimensional space (this time please actually do your best in order to get http://www.internationalskeptics.com/forums/showpost.php?p=7540470&postcount=16339)).

But you think that there is only one true card game -- some doron canasta --

Wrong, there are infinitely many context-dependent games (each game has its own rules) AND cross-contexts principle of being a game.

In other words, in this case you have failed to get "game" as the "host" cross-context mathematical space, and the infinitely many context-dependent games as the "hosted" mathematical spaces.

 

[doronshadmi]

Enjoy : http://www.youtube.com/watch?v=YOQb_mtkEEE&feature=related

 

[doronshadmi]

By using the fact that we are dealing with collections of distinct objects, let us re-search such collections by understanding notations according to verbal_symbolic AND visual_spatial skills.


The cardinality of Fullness is |{}| = ∞, where Fullness (that has no successor) is notated by the outer "{" and "}".

The cardinality of Emptiness is {||} = 0, where Emptiness (that has no predecessor) has no notation.

By understanding the difference between |{}| and {||}, we are able to deal with cardinality which is > {||} AND < |{}|, for example, such that {|...|} < |{...}|, where "..." is a general notation of members.

{|{}|} = 1

|{{}}| = ∞ because Fullness has no successor (its cardinality is inaccessible to all that have cardinality with successors (whether the amount of successors is finite or not).

Generally, all that have cardinality with successors, such cardinality is notated (for example) as {||}, {|a|}, {|a,b|}, {|a,b,c|} , ... etc. in the case of finite cardinality, or notated (for example) as {|,a,b,c,...|} in the case of infinite cardinality.

Russell's paradox is naturally solved as follows:

|{,a,b,c,...}| = ∞

{|,a,b,c,...|} < ∞

{|,{,a,b,c,...},a,b,c,...|} < ∞ = |{,{,a,b,c,...},a,b,c,...}|

Generally , the cardinality of all given collections with distinct objects < cardinality ∞.

So no collection of distinct objects can be its own member, because being a member of collection of distinct members, does not change the fact that the cardinality of all members of a given collection of distinct objects < ∞.

By understanding that (for example) cardinality |{,{,a,b,c,...},a,b,c,...}| > {|,{,a,b,c,...},a,b,c,...|} , one captures that no member (which is no more than "hosted" mathematical space) of a given collection (which is not less than "host" mathematical space) is equivalent to the given collection.

 

[zooterkin]

Generally , the cardinality of all given collections with distinct objects < cardinality ∞.

Are you saying that the cardinality of the set of positive integers (which are distinct objects) is not ∞?

 

[doronshadmi]

Are you saying that the cardinality of the set of positive integers (which are distinct objects) is not ∞?

∞ < ∞, where ∞ is the cardinality of Fullness (that has no successor) and ∞ is the cardinality of infinite collections on it (which are incomplete w.r.t to it, since no matter how infinitely many successors (immediate or non-immediate) they have, the cardinality of Fullness (∞) is inaccessible to them).

Fullness (that has no successor) is the "host" mathematical space, which is naturally beyond the power of all infinite collections (they have successors) which are "hosted" mathematical spaces on it.

By understanding this simple fact, it is realized that no collection of "hosted" mathematical spaces have the power of the "host" space, or in other words, the cardinality of the "hosted" mathematical spaces (and members are such spaces) < cardinality of the "host" space.

Fullness is shown, for example, by the non-locality of 1-dimensional "host" mathematical space w.r.t all infinite "hosted" mathematical spaces (whether they are infinite collections of points or line segments on it), which are local w.r.t the 1-dimensional "host" mathematical space.

As long as you do not get the mathematical science as Cross-contexts (Non-locality, or "host" mathematical space) AND Context-dependent (Locality, or "hosted" mathematical spaces) as a one comprehensive framework, you can't comprehend this post.

Once again, Cardinality is between the cardinality of Emptiness (that has no predecessor, which is notated as {||}) and the cardinality of Fullness (that has no successor, which is notated, at least, as |{}|).

Some claims: "1-dimensional mathematical space does not have the cardinality of fullness since it has, for example, 2-dimensional mathematical space as its successor, and so on ... ad infinituum".

Well, the important fact is the "host"\"hosted" principle between mathematical spaces, which is defined exactly because of the inaccessibility of the cardinality of Fullness to all mathematical spaces, which have successors (immediate or not).

Mathematical spaces are considered as collections w.r.t any given "host" mathematical space, which is derived from the "host"\"hosted" principle between mathematical spaces.

The existence of fundamental principle among infinitely many levels of a given non-trivial system, is actually one of the beauties of Cross-contexts AND Context-dependent framework.

Unity is the symmetry that prevents the distinction between Emptiness, Fullness, and everything between them.

 

[doronshadmi]

Let's correct the last paragraph of http://www.internationalskeptics.com/forums/showpost.php?p=7653835&postcount=16537.

Instead of

By understanding that (for example) cardinality |{,{,a,b,c,...},a,b,c,...}| > {|,{,a,b,c,...},a,b,c,...|} , one captures that no member (which is no more than "hosted" mathematical space) of a given collection (which is not less than "host" mathematical space) is equivalent to the given collection.

It has to be:

By understanding that (for example) cardinality |{,{,a,b,c,...},a,b,c,...}| > {|,{,a,b,c,...},a,b,c,...|} , one captures that no member (which is no more than "hosted" mathematical space) is equivalent to the "host" mathematical space.