Deeper than primes - Continuation

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More about verbal_symbolic AND visual_spatial brain skills:

According to my framework, expressions like "=" and "<" are derived from using verbal_symbolic AND visual_spatial brain skills.
 
doronshadmi said:
"01" is the simultaneous associations among 100% "0" AND 100% "1", which disallows the individual recognition of "0" OR "1".
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Let's explain it by using also visual_spatial brain skills.

There is a barrier
Code: 
___ _____
which allows the transition of things (horizontally w.r.t it) from one side to the other side, according to the size of a given opening.

A given thing is called certain if it can go from one side to the other side of the given barrier, otherwise it is uncertain.

0 OR 1 can do it.

01 can't do it.

In terms of verbal_symbolic brain skills the ratio 1/1 is certainty, where the ratio 2/1 is uncertainty, if associated with the visual_spatial brain skills, in this example.
 
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OK, let's try to explain this using visual_spatial skillz. Here ya go, doron, this explains all:



You're welcome.
 
This

322964e6fac5640bd3.jpg


is tasting WILLANS seat belt.

Verbal_symbolic AND visual_spatial brain skills are used, in order to interpret it.
 
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Dealing with 0.999... < 1 or 0.999... = 1 by using verbal_symbolic-only brain skills, is done in different frameworks, where one framework includes infinitesimals, and the other excludes infinitesimals.

So by using verbal_symbolic-only brain skills Math is no more than a collection of context-dependent frameworks, which are isolated of each other in order to avoid a contradiction like 0.999... < 1 AND 0.999... = 1.

By using also visual_spatial brain skills, which enables to understand the irreducibility of a given non-composed dimensional space > 0 into lower dimensional spaces, one actually develops the notion of infinity beyond the infinity that is derived from the concept of collection.

Furthermore, the stronger power of infinity that is derived from a given non-composed dimensional space > 0, enables to unify the understanding of infinity that is derived from the concept of collection, such that infinity at the level of collections is no more than a potential infinity w.r.t the actual infinity of a given non-composed dimensional space > 0.

By using this notion (that can't be known without using verbal_symbolic AND visual_spatial brain skills), Math opens the door for cross-contexts framework, which enables to consistently unify potential infinities frameworks, such that each framework is a consistent branch of a one comprehensive framework.

By using the unified framework (that can't be known without using verbal_symbolic AND visual_spatial brain skills), one enables to understand the failure of a framework that is based on the concept of collection that excludes infinitesimals, and one also enables to understand the rigorous basis (the irreducibility of a given non-composed dimensional space > 0 into lower dimensional spaces) that enables to assert infinitesimals.
 
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The infinitely large and the infinitely small are unified by a one principle, which is the irreducibility of a given non-composed dimensional space > 0 into lower dimensional spaces.

This principle can't be known unless verbal_symbolic AND visual_spatial brain skills are used.
 
Such researches ( http://math.coe.uga.edu/tme/Issues/v21n2/v21n2_Norton&Baldwin_Abs.html ) are easily resolved by using verbal_symbolic AND visual_spatial brain skills, which enable to understand the irreducibility of a given non-composed dimensional space > 0 into lower dimensional spaces.

According to this understanding a given non-composed dimensional space > 0 is actual infinity, where any amount of lower dimensional spaces on it is no more than potential infinity.
 
According to http://www.cut-the-knot.org/WhatIs/Infinity/HyperrealNumbers.shtml
0 < κ-1 < 1/n, or even
0 < κ-1 < a, for any real a > 0.
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If this is true, then there is no reason to stop here, and by using the same logic

0 < j-1 < 1/k, or even
0 < j-1 < a, for any real a > 0.
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etc. ... ad infinitum, such that n-1 > κ-1 > j-1 > ... > ... 0

In other words, no matter how many levels of infinitesimals are symbolized, no amount of them has the power of a given non-composed dimensional space > 0, which has the power of actual infinity (that can't be known by using verbal_symbolic-only brain skills).
 
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If you're forced to invent a plethora of new terms and redefine many others in order to make your hypothesis work, then perhaps you should scrap your hypothesis and start anew. What good is an idea if it requires you to reinvent the entirety of the universe before it's worth something?
 
Mister Earl said:
If you're forced to invent a plethora of new terms and redefine many others in order to make your hypothesis work, then perhaps you should scrap your hypothesis and start anew. What good is an idea if it requires you to reinvent the entirety of the universe before it's worth something?
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All is needed is to use visual_spatial brain skills in addition to verbal_symbolic brain skills.

Simple as that.

Can you do that?
 
doronshadmi said:
All is needed is to use visual_spatial brain skills in addition to verbal_symbolic brain skills.

Simple as that.

Can you do that?
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Absolutely. And when I do, it tells me that most of this thread is nothing more than random word salad. What I said before stands. Your premise here is only valid if you redefine the universe first. Having to do that should tell you that there's serious problems with your hypothesis. But let's ignore all of that now. What productive work can your hypothesis do that cannot also be done via a method that does not require redefining everything first?

Anything?
 
zooterkin said:
And your results from doing this are what, exactly?
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A paradigm-shift in the understanding of actual infinity, which has a direct influence on our understanding of Entropy in terms of open abstract or non-abstract realm.

Furthermore, analysis is unified by cross-contexts principle.
 
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doronshadmi said:
A paradigm-shift in the understanding of actual infinity, which has a direct result on our understanding of Entropy in terms of open abstract or non-abstract realm.

Furthermore, Mathematics is unified by cross-contexts principle.
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A great jumble of words that collectively mean nothing. Congratulations, Doronshadmi. You've succeeded in the same way the Indians did in the 9th century.
 
I think, rather, that the issue is that I *do* have it, and that I have a better gauge of it's worth.

I'm sorry, doronshadmi, but personal preference has no facet in science or truth. Either something is or it is not. Given that this is your hypothesis, the onus is on you to prove it works. A rational scientist, for contrast purposes here, would listen to and then address the concerns of other people pointing out the flaws. The scientist would do this because the hypothesis doesn't work if the flaws aren't addressed. This might involve changing or discarding the hypothesis. Now, you, on the other hand, don't bother to correct those flaws. Instead you use tactics like inventing new words or redefining old ones. Not to correct, but to conceal.

This is why you fail. You will not and can not progress until this is corrected. Again, personal preference does not factor in. You will not make your hypothesis truer by repetition.
 
Here is what I have gathered about doronetics (is that doron's word, or a joke someone else came up with?):

The main axiom is that spaces are simple, in the sense that they do not have parts. In particular, a one dimensional space is not composed of points, a two dimensional space is not composed of one dimensional spaces or of points, etc. However, there is an overlapping relation among spaces. While a space cannot be part of another space, they can overlap. So you can keep cramming points onto a line forever. So far, this idea is at least coherent (though ironically enough, I make that judgment using primarily symbolic reasoning). I am sure a coherent system of geometry or analysis could be constructed based on axioms about non-composed spaces and their relations.

A couple of things to note: (1) many supposed "results" doron has touted turn out just to be restatements of the axiom of the simplicity of spaces. (2) As long as we can talk about spaces overlapping other spaces, the standard real line exists as a collection of points along a 1D space. All of real analysis will be true of this structure, so there is no cause for concern on the part of traditional mathematics (including the dreaded 0.999...=1).

As mentioned several times, there is no particular reason to be excited about assuming spaces are not composed of parts unless we can prove some interesting results from it. As far as I can tell, this has not happened.

Personally, thinking spatially I see no reason to prefer simple spaces to standard spaces.
 
BenjaminTR said:
Personally, thinking spatially I see no reason to prefer simple spaces to standard spaces.
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What you call standard spaces, are composed results among what you call simple spaces, such that no amount of lower standard spaces or lower simple spaces have the power of a given higher simple space > 0.

So you do not have to prefer simple spaces to standard spaces, because a given simple space > 0 is an actual infinity with respect to lower standard spaces on it, where standard spaces on a given higher simple space > 0 (or collections of lower simple spaces on a given higher simple space > 0) are potential infinity with respect to a given higher simple space > 0.

In general, all the powers of given collections on a given higher simple space > 0 are < than the power of that higher simple space > 0.

In other words, there is a paradigm-shift in the understanding of actual infinity[1] (that can't be known, unless one uses at least verbal_symbolic AND visual_spatial brain skills) which enables to unify all collections under the notion of potential infinity, where this notion, in terms of analysis is symbolically expressed as "n-1 > κ-1 > j-1 > ... > ... 0" (where this expression can't be really understood without using also visual_spatial brain skills, in order to deal with simple higher spaces and their actual power of infinity).

The infinitely large and the infinitely small are unified by a one principle, which is the irreducibility of a given non-composed dimensional space > 0 into lower dimensional spaces on it (whether these lower dimensional spaces are non-composed (simple lower spaces) or composed (standard lower spaces)).

BenjaminTR said:
All of real analysis will be true of this structure, so there is no cause for concern on the part of traditional mathematics (including the dreaded 0.999...=1).
Click to expand...

I are wrong, by using the unified framework (that can't be known without using verbal_symbolic AND visual_spatial brain skills), one enables to understand the failure of a framework that is based on the concept of collection that excludes infinitesimals, and one also enables to understand the rigorous basis (the irreducibility of a given non-composed dimensional space > 0 into lower dimensional spaces) that enables to assert infinitesimals, in the first place.

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[1] For more details, please look at http://www.internationalskeptics.com/forums/showpost.php?p=9170466&postcount=2248 and http://www.internationalskeptics.com/forums/showpost.php?p=9170658&postcount=2249.
 
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Mister Earl said:
Sounds almost like a redefinition done tautologically but via obfuscation.
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Actual infinity is strictly distinguished from potential infinity if one uses verbal_symbolic AND visual_spatial brain skills, when dealing with the considered subject.
 
doronshadmi said:
Actual infinity is strictly distinguished from potential infinity if one uses verbal_symbolic AND visual_spatial brain skills, when dealing with the considered subject.
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ROFL What an utter pile of meaningless crap!
 
BenjaminTR said:
... (though ironically enough, I make that judgment using primarily symbolic reasoning).
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Yet, you can't completely avoid also spatial reasoning to make that judgment, so there is no irony.

Using verbal_symbolic AND visual_spatial brain skills does not determine how much brain skills > 0 of them is used.
 
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BenjaminTR said:
... doronetics (is that doron's word, or a joke someone else came up with?)...
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I dubbed it "Doronetics." Seemed fitting, all in all. The "organic mathematics" moniker is Doron's which I believe he contrived from a presentation of Hilbert, totally misunderstood by Doron.
 
Organic Mathematics is based on the notion of the consistent relations among the organs of the same organism, such that no organ contradict any other organ.

This is not the case with different frameworks of Mathematics, as it is currently understood by the majority of "pure" mathematicians, where one of the distinct examples is the two context-dependent frameworks of Standard and Non-standard Analysis, that can't be considered as organs or branches of the same organism, in order to avoid "0.999... < 1 AND 0.999... = 1" inconsistent expression.

As for Hilbert, he used the term organism at the end of his ICM 1900 Paris lecture, as follows:

"The problems mentioned are merely samples of problems, yet they will suffice to show how rich, how manifold and how extensive the mathematical science of today is, and the question is urged upon us whether mathematics is doomed to the fate of those other sciences that have split up into separate branches, whose representatives scarcely understand one another and whose connection becomes ever more loose. I do not believe this nor wish it. Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.

But, we ask, with the extension of mathematical knowledge will it not finally become impossible for the single investigator to embrace all departments of this knowledge? In answer let me point out how thoroughly it is ingrained in mathematical science that every real advance goes hand in hand with the invention of sharper tools and simpler methods which at the same time assist in understanding earlier theories and cast aside older more complicated developments. It is therefore possible for the individual investigator, when he makes these sharper tools and simpler methods his own, to find his way more easily in the various branches of mathematics than is possible in any other science.

The organic unity of mathematics is inherent in the nature of this science, for mathematics is the foundation of all exact knowledge of natural phenomena. That it may completely fulfill this high mission, may the new century bring it gifted masters and many zealous and enthusiastic disciples!" ( http://www.clarku.edu/~djoyce/hilbert/ )

In my opinion, his view of "The organic unity of mathematics" is the right view, but unfortunately can't be fulfilled by the paradigm of context-dependent-only frameworks, which are isolated of each other in order to avoid inconsistency (as seen in the example above).
 
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If one were to read and comprehend the actual presentation Hilbert gave, one would see that Hilbert was arguing against Mathematics partitioning itself into a collection of specialty fields. Through several examples, he showed how developments in one branch of Mathematics could have significant impact on another, seemingly unrelated branch in unexpected and delightful ways.

His point, the basis of his organic metaphor, was that Mathematics is an interconnected whole.

Hilbert was not advocating the sort of nonsense DoronShadmi advocates. DoronShadmi would forbid where Hilbert would embrace diversity among and within the branches.
 
jsfisher said:
If one were to read and comprehend the actual presentation Hilbert gave, one would see that Hilbert was arguing against Mathematics partitioning itself into a collection of specialty fields. Through several examples, he showed how developments in one branch of Mathematics could have significant impact on another, seemingly unrelated branch in unexpected and delightful ways.

His point, the basis of his organic metaphor, was that Mathematics is an interconnected whole.

Hilbert was not advocating the sort of nonsense DoronShadmi advocates. DoronShadmi would forbid where Hilbert would embrace diversity among and within the branches.
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According to the principles of Evolution not all things survive during natural selection, especially if they block the development of further diversity.

For example, "0.999... = 1" block does not survive the diversity of infinitely levels of infinitesimals, as seen in "n-1 > κ-1 > j-1 > ... > ... 0" (where this expression can't be really understood without using also visual_spatial brain skills, in order to deal with non-composed higher dimensional spaces > 0 and their actual power of infinity).

The infinitely large and the infinitely small are unified by a one principle, which is the irreducibility of a given non-composed dimensional space > 0 into lower dimensional spaces on it (whether these lower dimensional spaces are non-composed (simple lower spaces) or composed (standard lower spaces)), and this is a concrete demonstration of "The organic unity of mathematics".

The diversity of the traditional mathematician here is the result of saving any given nonsense (and in this case "n-1 > 0" (where "> κ-1 > j-1 > ... > ..." are arbitrarily excluded) nonsensical framework (which is derived from using verbal_symbolic-only brain skills) is equivalent to the ignorance of Pythagoras about the irrational numbers).
 
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BenjaminTR said:
...
Second, I would love a link to the discussion of 2 and sets containing 2 as a member.
...
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Sorry for the delay getting back on this. Here are a couple links to absurd things Doronshadmi has posted regarding set membership:

http://www.internationalskeptics.com/forums/showpost.php?p=3854589&postcount=1610
Doron confirms that 2 is not a member of { 2 } and that 1/4 and 0.25 are not the same number.

http://www.internationalskeptics.com/forums/showpost.php?p=3854952&postcount=1618
Doron confirms that 2 is and isn't a member of { 2 } and that a set is the union of its members.

And then there is my favorite:
http://www.internationalskeptics.com/forums/showpost.php?p=3571912&postcount=220
Doron explains in his own words how 2 is not part of { 2,3,4 } much like a severed finger is not part of your body.
 
jsfisher said:
Sorry for the delay getting back on this. Here are a couple links to absurd things Doronshadmi has posted regarding set membership:

http://www.internationalskeptics.com/forums/showpost.php?p=3854589&postcount=1610
Doron confirms that 2 is not a member of { 2 } and that 1/4 and 0.25 are not the same number.

http://www.internationalskeptics.com/forums/showpost.php?p=3854952&postcount=1618
Doron confirms that 2 is and isn't a member of { 2 } and that a set is the union of its members.

And then there is my favorite:
http://www.internationalskeptics.com/forums/showpost.php?p=3571912&postcount=220
Doron explains in his own words how 2 is not part of { 2,3,4 } much like a severed finger is not part of your body.
Click to expand...
What is there to say to that? Um...

There is this: apparently 2={2}. Kind of. Or it does, but it does not. Anyway, if everything is identical to its own singleton, then a set is the union of its members! As long as you ignore set theory axioms. No matter, no one likes the axiom of foundation anyway. It also helps not to be bothered by direct contradictions (2 is not a member of any set and is a member of some set).

Thanks for the links. Educational.
 
BenjaminTR said:
What is there to say to that? Um...

There is this: apparently 2={2}. Kind of. Or it does, but it does not. Anyway, if everything is identical to its own singleton, then a set is the union of its members! As long as you ignore set theory axioms. No matter, no one likes the axiom of foundation anyway. It also helps not to be bothered by direct contradictions (2 is not a member of any set and is a member of some set).

Thanks for the links. Educational.
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2 is not a member of any set at membership level 0 or it is a member of some set at membership level > 0.

You simply ignored this discussed subject in http://www.internationalskeptics.com/forums/showpost.php?p=9193272&postcount=2318.

Even more detailed stuff is shown if one reads http://www.scribd.com/doc/98276640/Umes pages 6 - 11.
 
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BenjaminTR said:
There is this: apparently 2={2}. Kind of. Or it does, but it does not. Anyway, if everything is identical to its own singleton, then a set is the union of its members!
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Wrong, 2 is an example of membership 0 level, where {2} is an example of membership > 0 level.

A given set's membership is derived from the union of its members, where its members are always objects of lower membership levels (so 2={2} is your wrong interpretation of membership levels, which according to it 2={2} does not hold).

Some example: {2,{3}} members are objects of membership 0 and 1 levels, where {2,{3}} membership is the union of lower membership levels etc., where there is no limitation to the complexity of lower membership levels under some set's union.

By following this reasoning {} "members" are below membership 0 level (or in other words, there are no members at all).
 
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doronshadmi said:
Wrong, 2 is an example of membership 0 level, where {2} is an example of membership > 0 level.

A given set's membership is derived from the union of its members, where its members are always objects of lower membership levels (so 2={2} is your wrong interpretation of membership levels, which according to it 2={2} does not hold).

Some example: {2,{3}} members are objects of membership 0 and 1 levels, where {2,{3}} membership is the union of lower membership levels etc., where there is no limitation to the complexity of lower membership levels under some set's union.

By following this reasoning {} "members" are below membership 0 level (or in other words, there are no members at all).
Click to expand...

So, is 2 a member of {2} ?
 
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