Deeper than primes

[WildCat]

I'm going to advise people not to respond to this thread. doronshadmi has a history of being totally incomprehensible and his threads always go for dozens of pages without any progress being made.

I don't think that will happen this time.

 

[ddt]

I don't think that will happen this time.

You're adding to the "Year in Review"? Alkatran's comment was from September 30th - 2008.

 

[ddt]

All of the stuff is saved. The problem is that it cannot be seen anymore in the old posts of this forum. I'll ask the moderator to give me the ability to change the Geocities addresses to new addresses, where my stuff can be found.

You're serious about that? Hell freezes over before the moderator would allow that. And where are you going to put them next? On another el-cheapo website that closes down when it feels like it? You should have put your money where your mouth is, and shelled out a couple of bucks for your own domain name.

 

[zooterkin]

When I say you should accept it, I mean there is a problem if you do not, a problem with mathematics.
...

Ah, the innocence of youth, or perhaps the naïveté of the noob...

Welcome, Sanelunatic. I wish you better luck than the rest of us have had in teaching Doron something about maths.

 

[six7s]

While I still have much to say, I will limit my post to talking about a few topics for the moment, and if discussion here is fruitful we can branch back out to other things. Furthermore, for the moment, I will drop my points about the real line and Zeno's paradox (for the moment, mind you!). I feel that neither of us will be able to convince the other of anything unless we both have a firm understanding of the other's ideas.

You do acknowledge that you risk having your head asplode, right?

On a more serious note: BRAVO! Superb post Welcome!

 

[doronshadmi]

There are mathematical systems that do not use some of the laws, for non-accusative algebra, non-commutative algebra, non-commutative geometry etc.

About Closure as a must-have term in general, please read about "Warning Signs of a Possible Collapse of Contemporary mathematics" http://www.math.princeton.edu/~nelson/papers/warn.pdf by Edward Nelson ( http://en.wikipedia.org/wiki/Edward_Nelson ).

Here is some quote from his paper:

For any specific numeral SSS. . . 0 we can indeed prove that it is an exponentiable number, but we cannot prove that the world of exponentiable numbers is closed under exponentiation. And superexponentiation leads us entirely away from the world of counting numbers.

The belief that exponentiation, superexponentiation, and so forth, applied to numerals yield numerals is just that—a belief. Here we have the third, and most serious, warning sign of trouble in contemporary mathematics.

Edward Nelson and most (if not all) mathematicians, understand Closure as a fundamental property of deductive systems, where each deductive system is first of all a closed framework, that is closed by a set of axioms, where any mathematical activity is done under Closure.

Godel, by using the axiomatic method showed that any axiomatic framework that is strong enough to deal with arithmetic, cannot be consistent AND complete.

It means that in such strong axiomatic frameworks there are true statements expressible in these axiomatic frameworks that are un-provable by the axioms of these axiomatic frameworks.

If we wish to save the consistency of such strong frameworks, we have to accept incompleteness as a fundamental property of the mathematical science, because the most interesting mathematical systems are strong frameworks.

In other words, we seriously have to reconsider Closure as a must have principle of the mathematical science.

I choose Non-locality as a fundamental principle of strong axiomatic frameworks, such that there exist y with respect to framework X, such that y belongs (it is true under X) AND does not belong (it is un-provable under X) to X.

From this non-local view y belongs XOR does not belong to X, is a contradiction, exactly as local z belongs AND does not belong to X, is a contradiction.


Let n=1 to ∞ and let k=0 to n-1, where n or k are atoms (they are existing AND empty things, exactly as {} is an existing AND empty thing).

Definition1: Given n it belongs NXOR does not belong to k.

Definition 2: Given k it belongs XOR does not belong to n.

Since n or k are atoms, they are not elements of each other, such that they are independent under Membership.

Independent Membership enables the existence of atoms as building-blocks of some complex, where a complex is the result n AND k atoms (no complex is only n or only k).

Now back to the real-line, by this NXOR\XOR Logic (where A,Not-A are F,F or T,T in the case of Non-locality, or A,Not-A are F,T or T,F in the case of Locality http://www.scribd.com/doc/16542245/OMPT pages 26-29), any k-D is Local w.r.t any n-D, and any n-D is non-local w.r.t k-D, such that no collection of k-Ds is n-D, exactly because a collection is a complex (k-D AND n-D) (the existence of Many is a complex result of Non-locality\Locality Linkage).

Now please read again http://www.internationalskeptics.com/forums/showpost.php?p=5278829&postcount=6664 .

 

[Little 10 Toes]

I did.

A line (an edgeless line) is a 1-D atom.

A segment is a complex that is made of two kinds of atoms (1-D atom AND 0-D atom).

Well if a line is endless, and a point is not, how do you get a line segment?

 

[doronshadmi]

Well if a line is endless, and a point is not, how do you get a line segment?

By AND logical connective between 1-D and 0-D.

Each D is an atom and by AND connective we get a segment, which is a complex (1-D AND 0-D).

Complex is Many and no Many is a one atom.

 

[Little 10 Toes]

By AND logical connective between 1-D and 0-D.

Each D is an atom and by AND connective we get a segment, which is a complex (1-D AND 0-D).

Complex is Many and no Many is a one atom.

Ah, so a line segment is a infinite line with points on it.

 

[doronshadmi]

Ah, so a line segment is a infinite line with points on it.

No, a line segment is (one 1-D) AND (two 0-D).

 

[Little 10 Toes]

By AND logical connective between 1-D and 0-D.

Each D is an atom and by AND connective we get a segment, which is a complex (1-D AND 0-D).

Complex is Many and no Many is a one atom.

Each dimension is an atom? Oh, this is going to be good then.

How does one determine what "D" an atom is going to be?

Also, if a 1-d object is endless, why isn't a line segment (combonation of an endless line and two points) endless?

 

[doronshadmi]

Each dimension is an atom? Oh, this is going to be good then.

How does one determine what "D" an atom is going to be?

Also, if a 1-d object is endless, why isn't a line segment (combonation of an endless line and two points) endless?

Because no complex result of 1-D AND 0-D is actual end (0-D) or actual endless (1-D).

In general no infinitely many complexities are 1-D or 0-D.

 

[doronshadmi]

How does one determine what "D" an atom is going to be?

http://www.internationalskeptics.com/forums/showpost.php?p=5283576&postcount=6686

 

[jsfisher]

There are mathematical systems that do not use some of the laws, for non-accusative algebra, non-commutative algebra, non-commutative geometry etc.

Sanelunatic already said that in his post.

About Closure as a must-have term in general, please read about "Warning Signs of a Possible Collapse of Contemporary mathematics"....

Nelson's comments are not relevant to Sanelunatic's point. The closure of which Sanelunatic wrote is by axiom, so its proof is trivial.

Godel, by using the axiomatic method showed that any axiomatic framework that is strong enough to deal with arithmetic, cannot be consistent AND complete....

Please stay focused, Doron, or are you intentionally trying to obscure the facts by conflating two different senses of the term, complete?


[The rest of the nonsensical Doron post, mercifully snipped.]

 

[The Man]

There are mathematical systems that do not use some of the laws, for non-accusative algebra, non-commutative algebra, non-commutative geometry etc.

About Closure as a must-have term in general, please read about "Warning Signs of a Possible Collapse of Contemporary mathematics" http://www.math.princeton.edu/~nelson/papers/warn.pdf

by Edward Nelson ( http://en.wikipedia.org/wiki/Edward_Nelson ).

Here is some quote from his paper:



Edward Nelson and most (if not all) mathematicians, understand Closure as a fundamental property of deductive systems, where each deductive system is first of all a closed framework, that is closed by a set of axioms, where any mathematical activity is done under Closure.

Godel, by using the axiomatic method showed that any axiomatic framework that is strong enough to deal with arithmetic, cannot be consistent AND complete.

It means that in such strong axiomatic frameworks there are true statements expressible in these axiomatic frameworks that are un-provable by the axioms of these axiomatic frameworks.

If we wish to save the consistency of such strong frameworks, we have to accept incompleteness as a fundamental property of the mathematical science, because the most interesting mathematical systems are strong frameworks.

In other words, we seriously have to reconsider Closure as a must have principle of the mathematical science.

I choose Non-locality as a fundamental principle of strong axiomatic frameworks, such that there exist y with respect to framework X, such that y belongs (it is true under X) AND does not belong (it is un-provable under X) to X.

From this non-local view y belongs XOR does not belong to X, is a contradiction, exactly as local z belongs AND does not belong to X, is a contradiction.


Let n=1 to ∞ and let k=0 to n-1, where n or k are atoms (they are existing AND empty things, exactly as {} is existing AND empty thing).

Definition1: Given n it belongs NXOR does not belong to k.

Definition 2: Given k it belongs XOR does not belong to n.

Since n or k are atoms, they are not elements of each other, such that they are independent under Membership.

Independent Membership enables the existence of atoms as building-blocks of some complex, where a complex is the result n AND k atoms (no complex is only n or only k).

Now back to the real-line, by this NXOR\XOR Logic (where A,Not-A are F,F or T,T in the case of Non-locality, or A,Not-A are F,T or T,F in the case of Locality http://www.scribd.com/doc/16542245/OMPT pages 26-29), any k-D is Local w.r.t any n-D, and any n-D is non-local w.r.t k-D, such that no collection of k-Ds is n-D, exactly because a collection is a complex (k-D AND n-D) (the existence of Many is a complex result of Non-locality\Locality Linkage).

Now please read again http://www.internationalskeptics.com/forums/showpost.php?p=5278829&postcount=6664 .

Another quote from that same paper by Edward Nelson.

“How do we know that P is a consistent theory, free from contradiction?
That is, how do we know that we cannot prove both a formula and
its negation?”

And one from your post

From this non-local view y belongs XOR does not belong to X, is a contradiction, exactly as local z belongs AND does not belong to X, is a contradiction.

You may claim

If we wish to save the consistency of such strong frameworks, we have to accept incompleteness as a fundamental property of the mathematical science, because the most interesting mathematical systems are strong frameworks.

However, you seem to have missed the most important part. That the incompleteness only refers to the inability to prove or disprove the consistency of certain assertions making it an axiomatic framework. Conversely the lack of any consistency is a specific and provable part of your “belongs AND does not belong” assertion, thus your notions are completely inconsistent. Your purported “framework” is so demonstrably self contradictory that it is simply not framework of any form, thus you simply insert into it whatever claims that suit you. Like your ‘non-finite’ interpolation as a ‘non-finite’ energy source, since you think you have obtained consistency through simple incompleteness, yet the only thing that is complete about your claims are their specific and demonstrative lack of consistency.



This statement probably demonstrates the failure of your purported consistency most clearly.

I choose Non-locality as a fundamental principle of strong axiomatic frameworks, such that there exist y with respect to framework X, such that y belongs (it is true under X) AND does not belong (it is un-provable under X) to X.

If “belongs” means “(it is true under X)” then its negation of “does not belong” would mean that 'it is not true under X' thus it would be FALSE “under X”. That it is “true under X” or FALSE “under X” would be provable “under X”. That you claim “(it is un-provable under X)” renders your claim “that y belongs (it is true under X)” simply false or your claim “that y belongs (it is true under X)” renders your claim that “(it is un-provable under X)” simply false. Once again you belabor the trivially obvious that certain aspects are accepted as true that can not be proven as true within the theory does not make them ‘true and un-provable’ but simply accepted since they are un-provable. One could just as easily accept them as false, but then you would end up with a different framework. Your argument does not seem to be that you take those axioms as false, but simply that you confuse their acceptance as true as the term “belongs” with the negation of that term “does not belong” as being that their truth is Un-provable within the framework. The simple fact is that since they are un-provable under that framework then they must either be accepted or rejected by an axiomatic approach. ‘belongs and does not belong’ under some framework is a direct contradiction and completely self-inconsistent. Un-provable and accepted as true (or even false) under some framework is self consistent yet incomplete in the ability to demonstrate (the truth or falsehood) by proofs within the framework of all assertions required for that framework.


I think we have finally gotten to the crux of your confusion Doron. As expected it is simply the result of your inconsistent application of terminology (“belongs” means one thing and “does not belong” means something other than the negation of “belongs”).

 

[doronshadmi]

If “belongs” means “(it is true under X)” then its negation of “does not belong” would mean that 'it is not true under X'

Only by Local-only reasoning.

By using also Non-local reasoning “belongs” means “(it is true under X)” AND “does not belong to X” means "beyond X" and therefore "un-provable under X".

You can't get this beauty by your Local-only reasoning.

I think we have finally gotten to the crux of your confusion Doron. As expected it is simply the result of your inconsistent application of terminology (“belongs” means one thing and “does not belong” means something other than the negation of “belongs”).

Again we see how The Man gets everything only in terms of Local reasoning, and then gets the wrong conclusions about Non-locality\Locality reasoning.

Here is something which is beyond your Local-only reasoning:

0-D is an atom.

1-D is an atom.

0-D AND 1-D is a complex.

No complex can be only 0-D or only 1-D, because the 0-D property of (0-D AND 1-D) prevents from (0-D AND 1-D) to be 1-D (and as a result we get infinite extrapolation), and the 1-D property of (0-D AND 1-D) prevents from (0-D AND 1-D) to be 0-D (and as a result we get infinite interpolation).

This reasoning is beyond your Local-only reasoning The Man, and we see your unsuccessful struggle al along this thread to reduce Non-locality\Locality reasoning to Local-only reasoning.

There is nothing to add in your case.

 

[The Man]

Only by Local-only reasoning.

As opposed to your Loco-only reasoning, that you demonstrate below.

By using also Non-local reasoning “belongs” means “(it is true under X)” AND “does not belong to X” means "beyond X" and therefore "un-provable under X".

False “under X” is still the negation of “true under X” adding your “beyond X” does not change that, but that simple fact is beyond your Loco-only reasoning.

You can't get this beauty by your Local-only reasoning.

Dorons ubiquitous fall back “it’s not me, it’s you” position.

You can’t understand your own ugly and obvious problems by your Loco-only reasoning.

Each time your resort to simply labeling people with your “Local-only reasoning” assertion I will return the favor by identifying your Loco-only reasoning in my response.

Again we see how The Man gets everything only in terms of Local reasoning, and then gets the wrong conclusions about Non-locality\Locality reasoning.

So having stated above that in fact you use “”does not belong to X” means "beyond X" and therefore "un-provable under X”” which is something other then the negation of ““belongs” means “(it is true under X)”, exactly as I asserted. You then claim I got the “wrong conclusions about Non-locality\Locality reasoning”? I’m sure in your Loco-only reasoning affirming my assertion must some how convince you that I got “the wrong conclusions about Non-locality\Locality reasoning”, but in Non-loco-only reasoning you have simply affirmed my asserted conclusion

Here is something which is beyond your Local-only reasoning:

0-D is an atom.

1-D is an atom.

0-D AND 1-D is a complex.

No complex can be only 0-D or only 1-D, because the 0-D property of (0-D AND 1-D) prevents from (0-D AND 1-D) to be 1-D (and as a result we get infinite extrapolation), and the 1-D property of (0-D AND 1-D) prevents from (0-D AND 1-D) to be 0-D (and as a result we get infinite interpolation).

Clearly and entirely in the realm of your Loco-only reasoning.

This reasoning is beyond your Local-only reasoning The Man, and we see your unsuccessful struggle al along this thread to reduce Non-locality\Locality reasoning to Local-only reasoning.

I have had no such “struggle”, my only struggle on this thread has been to try and steer away from your Loco-only reasoning and into Non-loco-only reasoning. How about you? You’ve still got that on going struggle on this thread of trying to make sense of your own notions by simply not making sense.

There is nothing to add in your case.

Any time you can actually bring yourself to stop. However, you have shown time and time again that you simply can not bear to even just stop yourself. Hardly indicative of your notions improving anything or helping anyone if you can not even use your own notions to help yourself just help yourself.

 

[doronshadmi]

False “under X” is still the negation of “true under X” .

"False under X" is a direct result of your Local-only reasoning.

By using also Non-local reasoning y is a true statment under axiomatic system X (it belongs to X) but axiomatic system X is too weak in order to prove it, because y is also beyond axiomatic system X (it also does not belong to X).

This is exactly the essence of being non-local (y belongs AND does not belong to axiomatic system X).

Your Local-only reasoning is too weak, The Man.

Clearly and entirely in the realm of your Loco-only reasoning.

Changing names does not help you to understand what you read.

 

[doronshadmi]

The closure of which Sanelunatic wrote is by axiom, so its proof is trivial.

No, the axiom is based on a wrong notion, which is something that you do not get from your mechanic-formal training.

 

[jsfisher]

No, the axiom is based on a wrong notion, which is something that you do not get from your mechanic-formal training.

I'm sorry. I forgot that axiom was another of those terms you don't understand.