Deeper than primes

[jsfisher]

This post http://www.internationalskeptics.com/forums/showpost.php?p=3580353&postcount=300 may help you to get it.

Also you ignored what I wrote at http://www.internationalskeptics.com/forums/showpost.php?p=4120100&postcount=362 about the right version of our paper, and quated things from the wrong version.

More reading comprehension issues.

What you wrote, quoted above, has nothing to do with ddt post, nor my post that prompted it.

Here's the point: You and Moshe completely misrepresented what Hilbert said.

 

[doronshadmi]

Here's the point: You and Moshe completely misrepresented what Hilbert said.

No, you and ddt do not get it:

Again, you ignored this part of the lecture ( http://www.cs.arizona.edu/~rcs/hilbert-speech ):

But, we ask, with the extension of mathematical knowl-
edge will it not finally become impossible for the single in-
vestigator 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 thoeries and cast aside older more complicated de-
velopments. 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.
(my edit)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
fulfil this high mission, may the new century bring it gifted
masters and many zealous and enthusiastic disciples.

Hilbert was full of hope that the mathematical scince will save the connections between its parts, because he belived that "the organic unity of the mathematical science is inherent in the nature of this science".

It is well known that the current mathematical science is made of parts that do not talk with each other, and something has to be done in order to fufill Hilbert's viewpoint about The Organic Unity of Mathematics.

This is exactly the goal of works like:

http://www.geocities.com/complementarytheory/OM.pdf

http://www.geocities.com/complementarytheory/UR.pdf

 

[jsfisher]

No, you and ddt do not get it:

Again, you ignored this part of the lecture ( http://www.cs.arizona.edu/~rcs/hilbert-speech ):


Hilbert was full of hope that the mathematical scince will save the connections between it parts.

It is well known that the current mathematical science is made of parts that do not talk with each other, and something has to be done in order to fufill Hilbert's viewpoint about The organic unity of mathematics.

More reading comprehension issues, I see.

Read the whole speech. Hilbert cites multiple examples of where solutions found in one branch of Mathematics have found elegant application in other branches. Hilbert was celebrating the many seemingly disparate parts as they form a united whole.

Hilbert allusion to the organic was that of a complex organism with multiple, very different parts with complex interrelations. He argued against the Mathematics branches becoming too specialized and compartmentalized at the expense of interconnections between the branches.

You and Moshe have mistakenly argued Hilbert meant to unify Mathematics. He did not. He wanted to preserve its unity, which is an entirely different matter.

 

[ddt]

This post http://www.internationalskeptics.com/forums/showpost.php?p=3580353&postcount=300 may help you to get it.

Your paper should be self-explanatory.

Also you ignored this part of the lecture ( http://www.cs.arizona.edu/~rcs/hilbert-speech ):

[...]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.
(my edit)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.[...]

You edited the text of Hilbert's lecture??? If you just meant you bolded a part, you've spent long enough on internet fora to see how you should indicate that.

As to that sentence of Hilbert's: he asserts there is already "organic unity" in mathematics, no need to go look for it and invent some crazy stuff that should "unify" mathematics.

It is well known that the current mathematical science is made of parts that do not talk with each other, and something has to be done in order to fufill Hilbert's viewpoint about The organic unity of mathematics.

Says the ignoramus.

I asked you before (and of course you didn't answer): what techniques are used in the (classical) proof of the Prime Number Distribution Theorem?

And what's been used in proving the Poincaré Conjecture?

And what's being used for the latest cryptographic methods?

Also you ignored what I wrote at http://www.internationalskeptics.com/forums/showpost.php?p=4120100&postcount=362 about the right version of our paper, and quated things from the wrong version.

Then show the differences.

 

[doronshadmi]

More reading comprehension issues, I see.

Read the whole speech. Hilbert cites multiple examples of where solutions found in one branch of Mathematics have found elegant application in other branches. Hilbert was celebrating the many seemingly disparate parts as they form a united whole.

Hilbert allusion to the organic was that of a complex organism with multiple, very different parts with complex interrelations. He argued against the Mathematics branches becoming too specialized and compartmentalized at the expense of interconnections between the branches.

You and Moshe have mistakenly argued Hilbert meant to unify Mathematics. He did not. He wanted to preserve its unity, which is an entirely different matter.

No, he knew that in the near future the complexity will be so high and in order to avoid dis-communication and dis-connections between mathematical branches, sharper and simpler tools have to be developed in order to save the mathematical science as an organism.

He explicitly says:

Mathematical science is in my opinion an indivisible whole, an
organism whose vitality is conditioned upon the connection
of its parts.

The current mathematical scince is far from Hilbert's Organic Paradigm.

 

[jsfisher]

No, he knew that in the near future the complexity will be so high and in order to avoid dis-communication and dis-connections between mathematical branches, sharper and simpler tools have to be developed in order to save the mathematical science as an organism.

He explicitly says:


The current mathematical scince is far form Hilbert's Organic Paradigm.

You continue to conflate unity with unify.

 

[doronshadmi]

I asked you before (and of course you didn't answer): what techniques are used in the (classical) proof of the Prime Number Distribution Theorem?

And what's been used in proving the Poincaré Conjecture?

And what's being used for the latest cryptographic methods?

Hilbert's lecture was taken before Einstein's SRT and Godel's work, and his naïve Organic Paradigm was influenced by Newton's mechanic paradigm, his success to define a complete theory of axioms for Geometry, which led him to hope that Physics can be formalized by using deductive methods.

Also he hoped to show that the mathematical science can completely prove its own consistency.

After Gödel's work most of the mathematicians stopped to seek for a one comprehensive framework for the mathematical science, and developed different branches that a lot of them do not talk with each other.

 

[ddt]

Hilbert's lecture was taken before Einstein's SRT and Godel's work, and his naïve Organic Paradigm was influenced by Newton's mechanic paradigm, his success to define a complete theory of axioms for Geometry, which led him to hope that Physics can be formalized by using deductive methods.

Also he hoped to show that the mathematical science can completely prove its own consistency.

After Gödel's work most of the mathematicians stopped to seek for a one comprehensive framework for the mathematical science, and developed different branches that a lot of them do not talk with each other.

As usual, you didn't answer my questions. I repeat them:

I asked you before (and of course you didn't answer): what techniques are used in the (classical) proof of the Prime Number Distribution Theorem?

And what's been used in proving the Poincaré Conjecture?

And what's being used for the latest cryptographic methods?

 

[doronshadmi]

You continue to conflate unity with unify.

Hilbert talked about a state, not about an action, and so we are.

 

[doronshadmi]

As usual, you didn't answer my questions. I repeat them:

Plaese show the organic unity of these proofs and mathods.

Please show how Geomtery, Logic, ZF Set Theory, Real Analysis, Number Theory, etc... can be simply and naturally connected with each other, according to Hilbert's Orgainc paradigm.

 

[jsfisher]

Hilbert talked about a state, not about an action, and so we are.

Huh?

 

[jsfisher]

Doron, seriously. English is not your first language, right? Ok, fine, but if you don't understand something addressed to you, don't respond with just anything that occurs to you.

It makes you look really stupid to reply as you do with complete disregard to what was posted.

If something is unclear, ask for clarification. There's no dishonor in that.

 

[doronshadmi]

Doron, seriously. English is not your first language, right? Ok, fine, but if you don't understand something addressed to you, don't respond with just anything that occurs to you.

It makes you look really stupid to reply as you do with complete disregard to what was posted.

If something is unclear, ask for clarification. There's no dishonor in that.

Unity is a state.

Unify is an action.

We do not use unify in our edited version of our work ( http://www.geocities.com/complementarytheory/OM.pdf ).

 

[ddt]

Plaese show the organic unity of these proofs and mathods.

Please show how Geomtery, Logic, ZF Set Theory, Real Analysis, Number Theory, etc... can be simply and naturally connected with each other, according to Hilbert's Orgainc paradigm.

First answer my questions:

I asked you before (and of course you didn't answer): what techniques are used in the (classical) proof of the Prime Number Distribution Theorem?

And what's been used in proving the Poincaré Conjecture?

And what's being used for the latest cryptographic methods?

 

[doronshadmi]

First of all, it wasn't published on the FICMAC website..

You are right, my mistake (actually I am glad that this wrong version is not in FICMAC website).

 

[doronshadmi]

First answer my questions:

I don't know about any common basis that is involeved here.

If you know then please share it with us.

 

[ddt]

I don't know about any common basis that is involeved here.

Translated for the rest: you don't know anything actual about mathematics. If you had, you had at least looked up these things and tried to give an answer.

ETA: your "common basis" wording here betrays again your confusion between "unity" and "unify".

If you know then please share it with us.

That would be pearl before swine for one poster here, and superfluous for the rest.

 

[jsfisher]

I now offer up my own generalizations of Doron's MAF. Since they each contain MAF as a proper subset, I claim they are each more powerful than MAF.

Formulation #1:

Let f be an arbitrary function.
Let x, y, z, ... be arbitrary elements.​

An example of an EMAF (extended MAF) is f(x,y,z).

More generally,

Let A be an n-tuple of arbitrary elements, where n is arbitrary.​

All EMAF's are of the from f(A)


Formulation #2:

Let X be anything at all.

All EMAF's are of the form X.


Discussion:

In formulation #1, it is clear that any doron underbar relation _ can be expressed as a function f and any asterisk element * can be expressed as a lowercase letter. So, simple function notation contains all of doron's MAF as a proper subset. Moreover, since A is not restricted to be a finite tuple, EMAF's clearly cover notions and concepts outside those available in MAF.

In formulation #2, well, since X can be anything, all of doron's MAF is included as a proper subset, all of formulation #1 is included, and well, all of everything else is included, too.


Conclusion:

Although formulation #1, unlike doron's MAF, is consistent with standard mathematical notation formulation #2 has such expressive simplicity to be preferred for all applications.


See how easy it is to be deep?

 

[doronshadmi]

ETA: your "common basis" wording here betrays again your confusion between "unity" and "unify".

Please show us where Hibert uses the word "unify" in http://www.cs.arizona.edu/~rcs/hilbert-speech .

Now after my answer was given, please give your's:

Please show how Geomtery, Logic, ZF Set Theory, Real Analysis, Number Theory, etc... can be simply and naturally connected with each other, according to Hilbert's Orgainc paradigm.

 

[doronshadmi]

I now offer up my own generalizations of Doron's MAF. Since they each contain MAF as a proper subset, I claim they are each more powerful than MAF.

Formulation #1:

Let f be an arbitrary function.
Let x, y, z, ... be arbitrary elements.​

An example of an EMAF (extended MAF) is f(x,y,z).

More generally,

Let A be an n-tuple of arbitrary elements, where n is arbitrary.​

All EMAF's are of the from f(A)


Formulation #2:

Let X be anything at all.

All EMAF's are of the form X.


Discussion:

In formulation #1, it is clear that any doron underbar relation _ can be expressed as a function f and any asterisk element * can be expressed as a lowercase letter. So, simple function notation contains all of doron's MAF as a proper subset. Moreover, since A is not restricted to be a finite tuple, EMAF's clearly cover notions and concepts outside those available in MAF.

In formulation #2, well, since X can be anything, all of doron's MAF is included as a proper subset, all of formulation #1 is included, and well, all of everything else is included, too.


Conclusion:

Although formulation #1, unlike doron's MAF, is consistent with standard mathematical notation formulation #2 has such expressive simplicity to be preferred for all applications.


See how easy it is to be deep?

Again you used the particular case of clear distinction as the general case of your framework.

You still do not get MAF because by using MAF proper subsets are avoided.