Deeper than primes

[Apathia]

Dear Aphatia,

There must be some kind of interaction, which enables us to research; otherwise we are at Singularity (going beyond any interaction) which is a non-comparable (and non-researchable) state. The interaction is between Relation and Element, and we, as researchers, are a significant factor of this interaction, because we give it is meaning.

So MAF (which is not Singularity) is the "must have" state of any researchable framework.

By using it we get a "nice to have" researchable framework, which has some particular meaning given by the researcher.

For example:

By using MAF *__* one can give some meaning to MAF *__* by define * as Element and __ as Relation.

By using Distinction as MAF's first-order property we get:

* id is *, __            * id is __  
|                and     |                   
* id is *, __            * id is *

As can be seen, the meaning is related always to the Elements, where the Relation enables us to compare between the Elements and arrive to some conclusions according to certain rules given by us.

In this particular case MAF *__* (that has no particular meaning of its own) is used in order to research itself, where we, as researchers give it this particular meaning.

Some claims that, for example, by using MAF *__* in order to research itself, we are using a circular reasoning. This is not the case because by giving MAF a meaning we are no longer at the "trunk" state, but we are at the "branch" state (where MAF has some particular meaning).

Actually MAF *__* can get any wished meaning of any two comparable Elements, for example:

* id is True, False            * id is True  
|                      and     |                   
* id is True, False            * id is False

In both cases MAF *__* (that has no meaning of its own, until we give it its meaning) is used.

By using some MAF one gets the natural trunk for infinitely many branches (where each branch has its particular meaning), which helps him to stay tuned and not get some branch (some particular meaning) as if it is the only possibility.

Ah, there it is. Still there, as plain as a pikestaff with a head on it.
Water ice and frozen water.
And the substitution of the word, "interaction" for the word "relationship."

What's going on Doron? Why can't you just say, "Yes, I'm using a different way talking about my "nice to have," "must have state of any researchable framework." It's the same as my Complementarity thingy, just a different way of putting it."
Instead of throwing it all out when I communicate it in a way some of the other participants of this thread can see some sense to it and make some useful critiques?

Of course I still could only be seeing dancing faries.

 

[doronshadmi]

Ah, there it is. Still there, as plain as a pikestaff with a head on it.
Water ice and frozen water.
And the substitution of the word, "interaction" for the word "relationship."

What's going on Doron? Why can't you just say, "Yes, I'm using a different way talking about my "nice to have," "must have state of any researchable framework." It's the same as my Complementarity thingy, just a different way of putting it."
Instead of throwing it all out when I communicate it in a way some of the other participants of this thread can see some sense to it and make some useful critiques?

Of course I still could only be seeing dancing faries.

Dear Apathia,

Do you get the beauty of the meaningless form (MAF) as the "trunk" of infinitely many (meaningful) "branches" (where the researcher is a significant factor of any given meaning, and Distinction is a first-order property)?

 

[jsfisher]

Dear Apathia,

Do you get the beauty of the meaningless form (MAF) as the "trunk" of infinitely many (meaningful) "branches" (where the researcher is a significant factor of any given meaning, and Distinction is a first-order property)?

Dear Doron,

Do you get the triviality of the meaningless form (MAF) of the gibberish you spout?

 

[Apathia]

Dear Apathia,

Do you get the beauty of the meaningless form (MAF) as the "trunk" of infinitely many (meaningful) "branches" (where the researcher is a significant factor of any given meaning, and Distinction is a first-order property)?

Assuming that this MAF is the framework you have been trying to present for twenty some odd years, I see a rwo pronged root system and the potential for a very interesting lingustic-cultural tree that I've thougts of making an integral part of the next fantasy story world I create.

I would feel it "beautiful" if I found it the core Principle of my worldview that was the significance of everything.
I'm not finding it that.

But then I still can't counter the argument that I'm reading my own stuff into you and of whatever you are saying, I know nothing.
It's time for me to go dance with my own faires.

 

[doronshadmi]

I would feel it "beautiful" if I found it the core Principle of my worldview that was the significance of everything.
I'm not finding it that.

Great,

So please take the (meaningless) "trunk" and define your significant (meaningful) "branch".

No one else will do it for you, because you are a significant factor of any "branch".

 

[TMiguel]

great,

so please take the (meaningless) "trunk" and define your significant (meaningful) "branch".

No one else will do it for you, because you are a significant factor of any "branch".

where is the proof?

 

[ddt]

Consider:

E => E + T
E => T
T => T * F
T => F
F => ( E )
F => a

...where + * ( ) are all symbols with the normal meaning in mathematical expressions involving addition and subtraction, and "a" represents any possible number or variable.

Pretty basic stuff. This context-free language may seem to be an almost trivial abstraction for expressions. And so it would be, except it also conveys a structure and precedence for the arithmetic operations. This simple abstraction led directly to improvements in parsing of computer languages and compilation into executable computer code. Prior to this development in formal languages and automata theory, computer langauge translation involved very ad hoc, make-shift methods.

The abstraction adds value.

Excellent point to bring up (context-free) grammars and languages. They may indeed seem trivial for something simple as an arithmetic expression, or a logic proposition, but they're certainly not for a computer language, with its many constructs like if-then-else (think of the "dangling else" problem), definition of and call to procedures/functions, statement sequences, etc. And, as you note, even for a simple language like logic propositions, formally defining the language by production rules indicates priority and associativity of the respective operators.

IIRC, the first language to employ a formal language definition - in "Backus-Naur form" was ALGOL-60; and since, every programming language invented has used that in one form or another. The Pascal report has them in the form of "railroad diagrams". It has, in fact, been so influential that virtually no-one nowadays builds their parsers by hand but uses parser generators such as yacc; a rule in yacc essentially consists of the formal language production rule interspersed with snippets of C-code in which you then can do the static semantic stuff like type checking.

Actually, you can do even better than using just context-free languages. ALGOL-68 employed a 2-level Van Wijngaarden grammar in its definition, thus also capturing all the static semantics of the language: whereas the report of ALGOL-60 had to say in words that the types of the THEN and ELSE-parts had to be identical, the ALGOL-68 definition put this into the formal language definition. In fact, you can also use a 2-level grammar for the definition of operator expressions (ad-hoc syntax mine; I only focus now on the priority part, not the associativity):

expression ::= functioncall | operexpr(9) | ...
operexpr ::= operexpr(n-1) operator operexpr
operator(1) ::= "="
operator(2) ::= "==" | "!="
operator(3) ::= ">" |"<" | ...
operator(4) ::= "+" | "-" | ...
operator(5) ::= "*" | "/" | ...​

I actually once built a parser for Gofer (a Haskell dialect) in Gofer using the Parser Monad, and employed such a scheme for operator expressions. Unfortunately, it turned out to be so slow that I had to rewrite it to a simpler scheme and re-adjust an operator expression tree after parsing it

MAF's, on the other hand, trivialize. They don't reveal structure or hidden meaning. They do the opposite, in fact. But doron's eyes are closed.

Not only that, but looking at the above, MAF's aren't even properly defined. If the rule *_*_* is to be seen as a production rule from some formal language (where the rules for "element" * and "relation" _ are conspicuously absent), we have a typing problem. If it's to be seen as (*_*)_*, the left relation "acts" on the left and middle element and the result is a logical proposition, not an "element"... And the same problem arises if you put the parentheses to the right.

 

[doronshadmi]

http://www.fdavidpeat.com/bibliography/essays/nat-cog.htm

 

[jsfisher]

http://www.fdavidpeat.com/bibliography/essays/nat-cog.htm

Are you trying to make a point? If you'd like to draw so parallels between your gibberish and the content of that website, please do so. Don't expect us to argue your case for you. You need to establish the connections.

Be careful, though. Be sure you want to be tied down by what's presented at that link.

 

[doronshadmi]

( http://www.fdavidpeat.com/bibliography/essays/nat-cog.htm )
While the quantum potential and the soliton can be discussed
using purely local mathematics, on the other hand David Bohm
has provided a powerful non-local metaphor for such systems
that he calls the Implicate (or enfolded) Order.9 What we take
for reality, Bohm argues, are surface phenomena, explicate
forms that have temporarily unfolded out of an underlying
implicate order. Within this deeper order forms are enfolded
within each other so systems which may be well separated in
the Explicate Order are contained within each other in the
Implicate Order. (my bold letters) Within the Implicate Order one form can be both interior and exterior to another.

[_] XOR [ ]_ (Locality)

[_]_ NXOR [_]_ (Non-Locality)

Non-Locality\Locality complementation.

 

[The Man]

Did you miss this part?

While the quantum potential and the soliton can be discussed
using purely local mathematics, on the other hand David Bohm
has provided a powerful non-local metaphor..

[_] XOR [ ]_ (Locality)

[_]_ NXOR [_]_ (Non-Locality)

Non-Locality\Locality complementation.

So is this your unnecessary and powerless “non-local metaphor”?

 

[doronshadmi]

Did you miss this part?

"Purely" local mathematics also uses non-locality, known as Relation.


Purely local mathematics is not researchable because each thing is totally isolated of any other thing.

The same holds if purely non-local mathematics is considered.

In this case no researchable things are comparable because all we have is Unity.

( http://www.fdavidpeat.com/bibliography/essays/nat-cog.htm )
Non-locality could be considered as a complementary description to that of locality, as part of a general nexus of new ideas, or as the starting point of a radically new approach to science.

About Prof. F. David Peat please look at http://en.wikipedia.org/wiki/F._David_Peat .

 

[The Man]

"Purely" local mathematics also uses non-locality, known as Relation.


Purely local mathematics is not researchable because each thing is totally isolated of any other thing.

The same holds if purely non-local mathematics is considered.

In this case no researchable things are comparable because all we have is Unity.



About Prof. F. David Peat please look at http://en.wikipedia.org/wiki/F._David_Peat .

So is that a yes or a no?

Non-locality complimenting locality is nothing new to science. A vector field is inherently non-local but can have an inherently local source such as the field from an electron.

 

[doronshadmi]

So is that a yes or a no?

Non-locality complimenting locality is nothing new to science. A vector field is inherently non-local but can have an inherently local source such as the field from an electron.

No.

If it is Non-Local it is the Relation between Locals, and no relation can be inherently Local, exactly as no Local can be inherently a Relation.

 

[jsfisher]

Yet another definition for non-local, eh?

So many contradictions, doron. It is really tough to keep track of them all.

 

[doronshadmi]

Yet another definition for non-local, eh?

So many contradictions, doron. It is really tough to keep track of them all.

The contradiction is a direct reuslt of your ability to get things only from their local point of view.

Wittgenstein already said ( http://www.science.uva.nl/~seop/entries/wittgenstein-mathematics/#WitIntCriSetThe ):

As Wittgenstein says at (MS 121, 71r; Dec. 27, 1938), three pages after the passage used for (RFM II, §57): “If you now call the Cantorian procedure one for producing a new real number, you will now no longer be inclined to speak of a system of all real numbers” (italics added). From Cantor's proof, however, set theorists erroneously conclude that “the set of irrational numbers” is greater in multiplicity than any enumeration of irrationals (or the set of rationals), when the only conclusion to draw is that there is no such thing as the set of all the irrational numbers. The truly dangerous aspect to ‘propositions’ such as “The real numbers cannot be arranged in a series” and “The set… is not denumerable” is that they make concept formation [i.e., our invention] “look like a fact of nature” (i.e., something we discover) (RFM II §§16, 37). At best, we have a vague idea of the concept of “real number,” but only if we restrict this idea to “recursive real number” and only if we recognize that having the concept does not mean having a set of all recursive real numbers.

But you simply unable to get that because you are a member a community of people that cannot get anything that is not local.

 

[jsfisher]

The contradiction is a direct reuslt of your ability to get things only from their local point of view.

...<snip meaningless aside>...

But you simply unable to get that because you are a member a community of people that cannot get anything that is not local.

No, the contradictions are strictly of your creation. You speak in gibberish, and you reason in reverse. Don't blame me or others when the problem is yours and yours alone.

 

[doronshadmi]

No, the contradictions are strictly of your creation. You speak in gibberish, and you reason in reverse. Don't blame me or others when the problem is yours and yours alone.

http://www.internationalskeptics.com/forums/showthread.php?t=125220 and Organic Mathematics is not for one-track minded.

Some link for non one-track minded: http://en.wikipedia.org/wiki/Holism_in_science

 

[jsfisher]

http://www.internationalskeptics.com/forums/showthread.php?t=125220 and Organic Mathematics is not for one-track minded.

I suppose organic is a plausible adjective given the high humus content.

Some link for non one-track minded: http://en.wikipedia.org/wiki/Holism_in_science

The wikipedia link leads to an article written in relatively straightforward English. It expresses complete thoughts in the form of sentences using generally accepted meanings of words. It is comprehensible.

It is nothing like your writings.

 

[TMiguel]

The contradiction is a direct reuslt of your ability to get things only from their local point of view.

Things or either are or are not. There is no “kind of is” in mathematical terms. If it means what we think it means that it is that what it means, if it doesn’t mean what we think it means, they you have to explain what it means.

As Wittgenstein says at (MS 121, 71r; Dec. 27, 1938), three pages after the passage used for (RFM II, §57): “If you now call the Cantorian procedure one for producing a new real number, you will now no longer be inclined to speak of a system of all real numbers” (italics added). From Cantor's proof, however, set theorists erroneously conclude that “the set of irrational numbers” is greater in multiplicity than any enumeration of irrationals (or the set of rationals), when the only conclusion to draw is that there is no such thing as the set of all the irrational numbers. The truly dangerous aspect to ‘propositions’ such as “The real numbers cannot be arranged in a series” and “The set… is not denumerable” is that they make concept formation [i.e., our invention] “look like a fact of nature” (i.e., something we discover) (RFM II §§16, 37). At best, we have a vague idea of the concept of “real number,” but only if we restrict this idea to “recursive real number” and only if we recognize that having the concept does not mean having a set of all recursive real numbers.

1. There is no “New Real Numbers”, there are real numbers and that’s it.
2. The irrational numbers is a R^2 relation. You do not conclude anything by enumeration because R is innumerable.

But you simply unable to get that because you are a member a community of people that cannot get anything that is not local.

Pure crap!