Deeper than primes

[zooterkin]

It was built by using only finite tools (no infinite extrapolation\interpolation).

I am talking about the technology beyond the finite, which starts by dealing with infinite extrapolation\interpolation, which are inherently incomplete.

You seem to have avoided this question:


Now, exactly what has ever been accomplished with OM?

 

[doronshadmi]

You seem to have avoided this question:


Now, exactly what has ever been accomplished with OM?

You do not get the answer.

As for the technology that enables computers, it is used now to accelerate the built-in dichotomy between Ethics and Logics, which can easily resulted by our self destruction in the near future, unless we develop the technology of the consciousness, where both Ethics AND Logics are complements of a one complex and inherently incomplete (and therefore naturally opened) reasoning, that its L value of Drake's equation (http://en.wikipedia.org/wiki/Drake_equation) is undefined.

 

[The Man]

X+X is the right incomplete series and X is the left incomplete series in the following diagram:

[qimg]http://farm3.static.flickr.com/2436/4394565223_68d292444a_o.jpg[/qimg]

Are you claiming X+X-X=X is invalid then?

Again your simple assumption that either of those series is “incomplete” does not make them incomplete. Nor do your futile attempts to simply make the word incomplete synonymous with infinite.

Again a circle, as a closed curve, is complete (it returns onto itself) so your use of circles (as does your insistence on closed curves) actually belies your assumption that they are incomplete.

http://www.internationalskeptics.com/forums/showpost.php?p=5668104&postcount=8872 your 3th part of your reply.

I never claimed you used the phrase “last segment” in that or any other post.

So again…

Excuse me ??

Where did I claim you used the phrase “'last segment” in that post?

Are you claiming that your “reaching segment” would not be the 'last segment' in that series for you?

 

[The Man]

You do not get the answer.

As for the technology that enables computers, it is used now to accelerate the built-in dichotomy between Ethics and Logics, which can easily resulted by our self destruction in the near future, unless we develop the technology of the consciousness, where both Ethics AND Logics are complements of a one complex and inherently incomplete (and therefore naturally opened) reasoning, that its L value of Drake's equation (http://en.wikipedia.org/wiki/Drake_equation) is undefined.

Again, do you even understand what the "L value of Drake's equation" represents?


Well I certainly have to grant you that "inherently incomplete <snip> reasoning" accurately describes your methods.

 

[doronshadmi]

The Man,

By trying to understand your view about my reasoning I find this:


You think that I interpret a converges geometric series like 1/2+1/4+1/8+… by using notions that are based on finite models.

You are wrong because a finite series like 1/2+1/4+1/8+ does not converge if it reaches a given limit (there are at least two segments of the same size in order to reach the value of the limit, but then the series does not converge, but simply reaches the value of the limit).

So we can't use a finite model when we deal with real convergence, where no two values of the same size are found in a series
like 1/2+1/4+1/8+ …

As a result real convergence is under the invariant state of being smaller, and this invariant property can't be found among any finite series.

The invariant state of being smaller is exactly the properly of real convergence and real convergence is expressed by an infinite series that can't reach a given limit (smaller means approaches, and no more than that).

 

[doronshadmi]

Again, do you even understand what the "L value of Drake's equation" represents?


Well I certainly have to grant you that "inherently incomplete <snip> reasoning" accurately describes your methods.

http://en.wikipedia.org/wiki/Drake_equation

L = the expected lifetime of such a civilization for the period that it can communicate across interstellar space

One of the reasons that L has a final value, is self destruction.

 

[doronshadmi]

Are you claiming X+X-X=X is invalid then?

No, I claim that X is incomplete if it is a series of the form 1/2+1/4+1/8+... or 1/1+1/2+1/4+...

Again your simple assumption that either of those series is “incomplete” does not make them incomplete.

It is not an assumption, it is an axiom that your reasoning can't get, because your reasoning is limited to the concept of Collection.

Again a circle, as a closed curve, is complete (it returns onto itself)

No, a circle is complete only if it has no points along it.

I never claimed you used the phrase “last segment” in that or any other post.

Really?

Try this:

Since your concept of a ‘last segment’ is inapplicable to the infinite series

 

[jsfisher]

It is a valid claim, your school of thouht plays a false game (1/∞ is defined to be 0 (written as 1/∞=0), but ∞*(1/∞) or ∞*0 of ∞*(1/∞)=∞*0 are undefined).

So you keep saying, and in so doing you continue to evade the question. You said that by standard mathematics...(0 = 1). You lied when you said that. It was by your own misunderstanding that you came to that bogus conclusion and then blamed everyone else for your failing.

By the way, since you don't care for Cantor's formulation, what would you like ∞*0 and ∞/∞ to be?

 

[sympathic]

More nonsense from a community of people that enable to deal with abstraction only by using a very limited and specific way.

In other words, this community of people dependents on specific tools, which actually are nothing but a reflection of their own limitations to deal with abstraction, which is actually independent on any specific tool.

Yes, we should probably add:

"proof by direct perception"

to the list. Doron: if you can't dance don't blame the floor.

 

[The Man]

http://en.wikipedia.org/wiki/Drake_equation

From the article you linked

L = the length of time such civilizations release detectable signals into space.

One of the reasons that L has a final value, is self destruction.

Doron there are plenty of reasons why a civilization may no longer “release detectable signals into space” or have never released “detectable signals into space” having nothing to do with “self destruction”. What is this morbid fixation you seem to have with our civilization and its “self destruction”? If you think your OM will stop the self destruction of our civilization then just say so, directly, but the “L” value in the Drake equation does not relate directly to self destruction, much as you might seem to enjoy thinking that it does.

 

[The Man]

No, I claim that X is incomplete if it is a series of the form 1/2+1/4+1/8+... or 1/1+1/2+1/4+...

Again a claim that has been proven to be wrong some 2,300 years ago. Again your simple claim that those series are “incomplete” does not make them incomplete.

It is not an assumption, it is an axiom that your reasoning can't get, because your reasoning is limited to the concept of Collection.

Just what do you think an axiom is other then something one assumes to be valid since it can not be proven or disproven within the given framework? Your “axiom” is just easily proven false for a convergent infinite series. You want to base you notion on false assumptions, that’s your problem.

Yes Doron we all know and understand you want them, so desperately, to be “incomplete” for your notions and will go to any length, including changing the meaning of complete so it just means finite. Again it just goes to show how blindly desperate you are to support your morbid fantasy of saving our civilization from its own self destruction.

No, a circle is complete only if it has no points along it.

Since you were unable to define your “closed curve” without points as you claimed you could, I doubt you will fare any better defining a circle without points. Again trying to make your “complete” synonymous with “no points” only goes to show how entirely contrived, self serving, superfluous and useless is your notion of “complete”.

Really?

Try this:

That certainly does not claim that you used the phrase “last segment” but simple labels the concept you were expounding as “your concept of a ‘last segment’”. Perhaps it is the use of single ‘ ‘ vs. the double “ “ quotation marks that is confusing you “ “ would indicate a quotation, if I was quoting you or some one else directly, ‘ ‘ would tend to indicate some particular and potentially obscure use of a term or phrase that perhaps is not directly quoted for some one. A convention I have used numerous times on this thread when dealing with your rather unique usages of words and phrases. “ “ indicating a direct quote of your usage and ‘ ‘ indicating my own paraphrasing of terms to fit within your typical usage. I can understand how you might have been confused, but since I have pointed out to you specifically again that I was not quoting you or claiming that you ever used that particular phrase, your continued insistence of such is just your problem.

 

[sympathic]

More nonsense from a community of people that enable to deal with abstraction only by using a very limited and specific way.

In other words, this community of people dependents on specific tools, which actually are nothing but a reflection of their own limitations to deal with abstraction, which is actually independent on any specific tool.

Reflection much?

 

[doronshadmi]

Again a claim that has been proven to be wrong some 2,300 years ago.

No The Man, it was not proven to be wrong some 2,300 years ago, exactly because Non-locality was not understood by Archimedes.

X+X-X=X does not say anything about the difference between the finite (that reaches the limit) and the infinite (that approaches the limit at its best).

I see that you have missed http://www.internationalskeptics.com/forums/showpost.php?p=5675046&postcount=8885

 

[sympathic]

No The Man, it was not proven to be wrong some 2,300 years ago, exactly because Non-locality was not understood by Archimedes.

X+X-X=X does not say anything about the difference between the finite (that reaches the limit) and the infinite (that approaches the limit at its best).

I see that you have missed http://www.internationalskeptics.com/forums/showpost.php?p=5675046&postcount=8885

Poor old Archimedes. Lucky for him JREF did not exist back then so he could not have been told he just did not get it.

 

[zooterkin]

I see that you have missed http://www.internationalskeptics.com/forums/showpost.php?p=5675046&postcount=8885

No, I suspect he was politely ignoring it.

 

[doronshadmi]

Just what do you think an axiom is other then something one assumes to be valid since it can not be proven or disproven within the given framework?

Question: Just what you think is the reason of your limitation to get completeness in terms of a pointless circle?

Answer: your inability to get things that are not Collections.

Yes Doron we all know and understand you want them, so desperately, to be “incomplete” for your notions and will go to any length, including changing the meaning of complete so it just means finite.

Wrong.

At the moment that you understand a pointless circle, then and only then you can easily understand that this completeness is the base ground for accurate values (which are finite) or inaccurate values (which are infinite).

A pointless circle is totally complete because is has no beginning AND no end (it has an atomic quality).

A circle with a single point along it defines a segment, and a closed segment is less complete than a pointless circle (completeness is a matter of Quality and not a matter of Quantity).

When more and more segments are used in order to define a circle, it becomes less and less complete, but as long as the amount of segments is finite, their added values have an accurate result known as Sum.

If an infinite amount of segments is used in order to define a circle, then also the accuracy of the result is lost and we do not have a Sum.

The best result of this inherent incompleteness is defined by an invariant proportion, which is possible exactly because at real convergence no two values of the same size are found in a series like 1/2+1/4+1/8+ … and this is an axiomatic fact that your limited reasoning simply can’t grasp.

Again it just goes to show how blindly desperate you are to support your morbid fantasy of saving our civilization from its own self destruction.

Again it is shown why OM’s reasoning of EEM ( http://www.scribd.com/doc/16547236/EEM ) is desperately needed exactly because of blind and dogmatic scholars like you.

 

[zooterkin]

Question: Just what you think is the reason of your limitation to get completeness in terms of a pointless circle?
...
At the moment that you understand a pointless circle, then and only then you can easily understand that this completeness is the base ground for accurate values (which are finite) or inaccurate values (which are infinite).

A pointless circle is totally complete because is has no beginning AND no end (it has an atomic quality).

A circle with a single point along it defines a segment, and a closed segment is less complete than a pointless circle (completeness is a matter of Quality and not a matter of Quantity).

When more and more segments are used in order to define a circle, it becomes less and less complete, but as long as the amount of segments is finite, their added values have an accurate result known as Sum.

Oh, dear, here we go again. You're parading your ignorance for all to see, Doron.


How do you define a circle without using any points? Go on, please define a circle; how big is it, and where is it? How do you avoid there being any points on it?


Choosing points on a circle does not alter how the circle is defined; choosing a point does not create a gap in the circle.

 

[The Man]

No The Man, it was not proven to be wrong some 2,300 years ago, exactly because Non-locality was not understood by Archimedes.

X+X-X=X does not say anything about the difference between the finite (that reaches the limit) and the infinite (that approaches the limit at its best).

It in fact shows that the difference between the two self similar infinite convergent series is finite, that difference being the sum (particularly in the ½ common ratio series) of one of those self similar infinite series.

Again your simple assumption that “the infinite (that approaches the limit at its best)” is specifically what it proves false.

I see that you have missed http://www.internationalskeptics.com/forums/showpost.php?p=5675046&postcount=8885

No, I suspect he was politely ignoring it.

Actually he is correct , I did not see that post. However having seen it now I would have most likely just politely ignored it had I seen it then.

If you are insisting on some remarks Doron I can certainly oblige.

The Man,

By trying to understand your view about my reasoning I find this:


You think that I interpret a converges geometric series like 1/2+1/4+1/8+… by using notions that are based on finite models.

That was your assertion with your “reaching segment” requirement.

You are wrong because a finite series like 1/2+1/4+1/8+ does not converge if it reaches a given limit (there are at least two segments of the same size in order to reach the value of the limit, but then the series does not converge, but simply reaches the value of the limit).

So we can't use a finite model when we deal with real convergence, where no two values of the same size are found in a series
like 1/2+1/4+1/8+ …

As a result real convergence is under the invariant state of being smaller, and this invariant property can't be found among any finite series.

The invariant state of being smaller is exactly the properly of real convergence and real convergence is expressed by an infinite series that can't reach a given limit (smaller means approaches, and no more than that).

Again a partial sum of the infinite series like “1/2+1/4+1/8” still leaves a self similar infinite series as the remainder of the original infinite series. That self similar infinite series converges to a sum equal to the difference between the partial sum and the limit. Your “reaching segment” is just an infinite series of self similar segments, just as the entire original self similar infinite convergent series is.

 

[The Man]

Question: Just what you think is the reason of your limitation to get completeness in terms of a pointless circle?

Answer: your inability to get things that are not Collections.

Nope just your inability to define a circle or any closed curve without points.

Wrong.

At the moment that you understand a pointless circle, then and only then you can easily understand that this completeness is the base ground for accurate values (which are finite) or inaccurate values (which are infinite).

Again the difference between the two self similar infinite convergent series is finite, accurate and complete as the sum of one of those series.

A pointless circle is totally complete because is has no beginning AND no end (it has an atomic quality).


A circle with a single point along it defines a segment, and a closed segment is less complete than a pointless circle (completeness is a matter of Quality and not a matter of Quantity).

Again complete refers specifically to the fact that nothing is missing that should be included. It is not a matter of “Quality” or “Quantity”, but simply inclusion or exclusion.

When more and more segments are used in order to define a circle, it becomes less and less complete, but as long as the amount of segments is finite, their added values have an accurate result known as Sum.

If an infinite amount of segments is used in order to define a circle, then also the accuracy of the result is lost and we do not have a Sum.

Again an infinite convergent series also has a sum that is both accurate and finite. Proven some 2,300 years ago.

The best result of this inherent incompleteness is defined by an invariant proportion, which is possible exactly because at real convergence no two values of the same size are found in a series like 1/2+1/4+1/8+ … and this is an axiomatic fact that your limited reasoning simply can’t grasp.

Again simply an assumption (your “two values of the same size” requirement) you base on a finite number of values and again proven wrong some 2,300 years ago for an infinite convergent series.

Again it is shown why OM’s reasoning of EEM ( http://www.scribd.com/doc/16547236/EEM ) is desperately needed exactly because of blind and dogmatic scholars like you.

Again it just goes to show how blindly desperate you are to support your morbid fantasy of saving our civilization from its own self destruction.

 

[doronshadmi]

Again complete refers specifically to the fact that nothing is missing that should be included.

Wrong.

Complete refers to a non-composed thing (atomic) , where inclusion or exclusion refer to composed things, which are incomplete w.r.t to the non-composed.

Again your notion does not distinguish between the complete (the atomic) and the incomplete (the non-atomic) where this distinction is based on the qualitative difference between the atomic and the composed.

A point or a line are atomic exactly because no one of them is made by the other. The line is the simplest example of a non-local atomic quality and a point is the simplest example of a local atomic quality.

By your quantitative-only notion you count them and conclude that the thing that includes them is non-atomic.

You are right about that, because that thing is called a collection, and a collection is a non-atomic thing.

Since your abstraction ability can deal only with collections, you are unable to understand that the Non-local and Local atomic aspects are the minimal manifestations of the atomic state itself, which is beyond any manifestation (it is not Non-local AND not Local, or any other property that is used to define it).

Your “reaching segment” is just an infinite series of self similar segments, just as the entire original self similar infinite convergent series is.

Again, there is no such a thing like the entire collection of infinitely many things, exactly because the cardinality of infinitely many things (the 1+1+1+… form) has no sum, and it does not matter if things become smaller of bigger (in both cases biggest or smallest, do not hold).

That self similar infinite series converges to a sum equal to the difference between the partial sum and the limit.

Simply wrong.

If the sum between the limit and the partial sum equals to the partial sum you do not deal anymore with converge series, because you add two equal sizes to each other in order to reach the limit.

Converge series do no have any two equal sizes along it in order to be considered as a converge series. The sizes of converge series must be different from each other no matter how infinitely many scales are involved.

Archimedes did not understand the real nature self similarity over infinitely many scale levels. This self-similarity is defined only if being smaller is an invariant property upon infinitely many scale levels, which permanently prevent the value of a given limit.


This simple notion can easily be proven by researching, for example, Koch fractal.

Koch fractal is infinite only if there are infinitely many scale levels, where each scale level is represented by a given segment that is smaller than any arbitrary previous segment, for example:

The Koch fractal is an example of infinite extrapolation\interpolation of scale levels of the form …+1+1+1+… that has no sum.


The self similarity over scales clearly shown also by the following diagram, where the values 1,2,4,8,16,32,… etc. are not reached, ad infinituum: