Deeper than primes

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jsfisher said:
Ho?

Also, I noticed the rest of your post didn't support your position at all. Shall we just agree that 2+2=5 and continue from there?
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EDIT:

Also according to your view, if it is not useful for both of us, we have an agreement about 2+2=5.

In this particular case we both agree that 2+2=5 is not useful, so there is an agreement between us, after all.
 
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doronshadmi said:
EDIT:

Also according to your view, if it is not useful for both of us, we have an agreement about 2+2=5.

In this particular case we both agree that 2+2=5 is not useful, so there is an agreement between us, after all.
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Does this total lack of facility comprehending written language account for your abysmal knowledge of Mathematics?
 
jsfisher said:
Does this total lack of facility comprehending written language account for your abysmal knowledge of Mathematics?
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I think this is just another attempt to hijack the conversation to his ideas. He does that all the time.
 
Doron,

In some of your posts it seems to my reading that you are saying that a quantity in memory is non-local.
For example, I'm doing old style pen and paper addition and I have a ten to carry and add to the next column. I hold that in memory till I add it in the process of arriving at the sum of a given column.
Is it while still in memory "non-local?"

My difficulty with this is that it is simply and totally a quantity (not a quality), and it's merely in an off-site location, so to speak, and not in some state or realm of non-locality quality.

Are you saying that it's in a mental realm and therefore qualitative?
That doesn't make much sense, because a mere quantity is also a mental construct.

There is an aspect of any given Organic Number that is merely quantitative.
And such is used in conventional arithmatic.
But there are aspects of a given Organic Number that are in part (in one of which is in toto) that are to some extent qualitative.

How is the qualitative aspect of 3 used in cognition?
Could you gave an example?
 
jsfisher said:
Does this total lack of facility comprehending written language account for your abysmal knowledge of Mathematics?
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You have to ask yourself this question, because you clearly demonstrate here a total lack of facility comprehending written language.
 
sympathic said:
I think this is just another attempt to hijack the conversation to his ideas. He does that all the time.
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Another example of a person that has a dogmatic view about some subject.

Any notion that does not follow the dogma is automatically interpreted as some attempt to hijack the conversation to frontiers that do not follow the agreed dogma.
 
Apathia said:
I hold that in memory till I add it in the process of arriving at the sum of a given column.
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1) You describe only the linear step-by-step use of Memory\Elements Interaction.

2) Memory is also the simultaneity of the connection of more than a one element.

3) Time is not necessarily involved here, so concepts like “process” are not fundamentals of Memory\Elements Interaction.

4) Again, please think again about the String\Beads analogy, the amount of elements is a simultaneous result of the String(Non-locality)\Bead(Locality) Interaction, which is independent of any step-by-step linear addition.

5) Usually addition is taken as a linear form because of the representation style that is based of x+y+z+... form.

6) But addition is independent of this particular representation, for example, by using Lisp programming language, addition is represented as
(+ x y z ...) where + is equivalent to the String and x y z ... are equivalent to Elements in String\Elements analogy.

7) In other words, please follow the notion and not any particular representation of it.
 
doronshadmi said:
You have to ask yourself this question, because you clearly demonstrate here a total lack of facility comprehending written language.
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You have demonstrated many times that merely writing something down does not automatically make it comprehensible.
 
doronshadmi said:
1) You describe only the linear step-by-step use of Memory\Elements Interaction.

2) Memory is also the simultaneity of the connection of more than a one element.

3) Time is not necessarily involved here, so concepts like “process” are not fundamentals of Memory\Elements Interaction.

4) Again, please think again about the String\Beads analogy, the amount of elements is a simultaneous result of the String(Non-locality)\Bead(Locality) Interaction, which is independent of any step-by-step linear addition.

5) Usually addition is taken as a linear form because of the representation style that is based of x+y+z+... form.

6) But addition is independent of this particular representation, for example, by using Lisp programming language, addition is represented as
(+ x y z ...) where + is equivalent to the String and x y z ... are equivalent to Elements in String\Elements analogy.

7) In other words, please follow the notion and not any particular representation of it.
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?????

I suppose I shouldn't have used the example I did.
My question was completly lost and not addressed.

Maybe I can salvage from it that number usage is a "Memory/Element Interaction" and is therefore non-linear.
And whatever is non-linear is non-local.
All words in the form of the phrase Word/Some Other Word Interaction are synomyms or restatements of the same thing.

A number is always a quality and a quantity, because it's of the Quantity/Quality Interaction.
 
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Apathia said:
How is the qualitative aspect of 3 used in cognition?
Could you gave an example?
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I suppose that the full answer to this question would be that 3 is a result of a Qualitative/Quantitative Interaction.
This could all be very interesting if there were more to it than merely that.
 
doronshadmi said:
What do you mean by "more to it than merely that"?
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The Organic Number Complex 3 intends to map out the forms of 3 in linear and non-linear thinking.
Could you please give a concrete example of how 3 is used in non-linear cognition.
Show how it works.

Merely repeating that an Organic Number is both elemental and relational, however fundamental that is to your approach to number, does not show how a complex works in application and in thinking.
 
doronshadmi said:
It was addressed.

No, a numerical value (accurate or not) is both quantity (elements) AND quality (relation).
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Fortunately I was able to cobble that together out of your oblique reply.

I want to see the circumstance when a number is used qualitative relationally, as opposed to the usual local only, element, quantity.
 
doronshadmi said:
No, the expression “0.000...1[base 2]” is incomplete and therefore smaller (it does not have an accurate value exactly as 0+1/2+1/4+1/8+1/16... (which is actually 0.1111...[base 2]) does not have an accurate value.

EDIT:

An expression like "0.000...1[base 2] is not understood in terms of "smaller than ..." but in terms of "permanently in a state of being smaller (can't be smallest)).

A local-only paradigm can't get that.
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“permanently in a state of being smaller” would make it the “smallest” in your notions. Are you claiming there is something smaller in your notions?


doronshadmi said:
All you did is to multiply values, where each one of them is accurate.
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What I (or more specifically Archimedes) did was multiply the series 1/2+1/4+1/8+1/16… by 2 meaning just adding it to itself.


doronshadmi said:
It does not mean that a collection of infinitely many accurate values that are added to each other is resulted by an accurate value (known as an accurate sum), exactly as 1+1+1+… form has no sum even if each added value is accurate.
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Again 1+1+1+1 is not a convergent series it is divergent. It demonstrates conclusively that you just don’t know (or apparently care) what you’re talking about. The relationships described by Archimedes conclusively demonstrate that the infinite convergent series 1/2+1/4+1/8+1/16… has a finite sum of 1. All you are doing is continuing to assert that the sum is not “an accurate value” yet you can not prove that assertion, while that infinite convergent series having a finite sum was proven some 2,300 years ago.



doronshadmi said:
A beautiful example of a non-scientific dogmatic paradigm, which like any religious approach actually says:

“Never re-search the past’s agreed knowledge, only pass it to the next generations as it is”.
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Doron you’re not researching anything you’re just making up crap and pretending it has some validity, yours is “A beautiful example of a non-scientific dogmatic paradigm”. If you had actually researched mathematics you would have found that it has changed quite extensively over the millennia. The fact that an infinite convergent geometric series has a demonstrable finite sum was just one of those changes. Again if you had actually bothered doing any research you might have know that, but instead you just prefer to operate under the delusion that you just making things up and assuming they are correct somehow constitutes research.
 
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Doron,

At some point after you tire of mumbling the same mantra, will you have anything actually useful to show us? So far it has just been "You don't get it," "Cantor was wrong," and your mindless repetition of contradiction and inconsistency.

Why can't you show us something with real utility?
 
The Man said:
“permanently in a state of being smaller” would make it the “smallest” in your notions.
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No, it would make it the “smallest” in your notions, The Man.

Furthermore, we can also understand "smaller than … in the usual sense, such that any arbitrary given size is > 0 AND smaller than any arbitrary previous size of an infinite series of distinct sizes.

In other words, the infinite series of added sizes is permanently smaller than the value of the given limit, no matter how many distinct sizes > 0 are involved.

Also please show us the proof of Archimedes about this subject.
 
Apathia said:
Fortunately I was able to cobble that together out of your oblique reply.

I want to see the circumstance when a number is used qualitative relationally, as opposed to the usual local only, element, quantity.
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Is there a particular reason of why do you continue to ignore, for example, http://www.scribd.com/doc/17039028/OMDP , http://www.scribd.com/doc/21967511/...considerations-of-Some-Mathematical-Paradigms or

4390093906_6c3ae0ab88_o.jpg

4389327007_f968923c21_o.jpg
 
zooterkin said:
You've already had it.
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This
The Man said:
What I (or more specifically Archimedes) did was multiply the series 1/2+1/4+1/8+1/16… by 2 meaning just adding it to itself.
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is not a proof that an infinite series of infinitely many distinct permanently smaller AND > 0 accurate sizes, has an accurate sum, which is equal to some accurate size, called limit.

It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2, so the second value after the stating point 0 is now 1/2*2= 1/1, the next value is now 1/4*2=1/2, etc… ad infinituum and now we simply do not reach the limit value 2 (before the multiplication we did not reach the limit value 1, so nothing was changed here, in both cases we do not reach the limit).
 
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doronshadmi said:
No, it would make it the “smallest” in your notions, The Man.
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Then you must have something smaller in your notions. What is it? Remember the questions was…

The Man said:
You contend that the convergent infinite sum never reaches the limit so it must have some “smallest segment” that is the difference between that infinite sum and the limit. So Doron what is your “smallest segment”?
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doronshadmi said:
Furthermore, we can also understand "smaller than … in the usual sense, such that any arbitrary given size is > 0 AND smaller than any arbitrary previous size of an infinite series of distinct sizes.
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So just what would “"smaller than …” mean in your ‘unusual sense’?

doronshadmi said:
In other words, the infinite series of added sizes is permanently smaller than the value of the given limit, no matter how many distinct sizes > 0 are involved.
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Already conclusively demonstrated to be false for a convergent infinite series some 2,300 years ago.


doronshadmi said:
Also please show us the proof of Archimedes about this subject.
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Already done numerous times, do some actual research yourself. Here is the link again as you seem to be unable to find it yourself.

http://en.wikipedia.org/wiki/Geometric_series#Sum
 
doronshadmi said:
This

is not a proof that an infinite series of infinitely many distinct permanently smaller AND > 0 accurate sizes, has an accurate sum, which is equal to some accurate size, called limit.

It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2, so the second value after the stating point 0 is now 1/2*2= 1/1, the next value is now 1/4*2=1/2, etc… ad infinituum and now we simply do not reach the limit value 2 (before the multiplication we did not reach the limit value 1, so nothing was changed here, in both cases we do not reach the limit).
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Much like analogies, Doron doesn't cope well with proofs, either.
 
doronshadmi said:
This

is not a proof that an infinite series of infinitely many distinct permanently smaller AND > 0 accurate sizes, has an accurate sum, which is equal to some accurate size, called limit.

It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2, so the second value after the stating point 0 is now 1/2*2= 1/1, the next value is now 1/4*2=1/2, etc… ad infinituum and now we simply do not reach the limit value 2 (before the multiplication we did not reach the limit value 1, so nothing was changed here, in both cases we do not reach the limit).
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Doron, again if you are asserting a circumference you are asserting that limit (the circumference) is being reached. Otherwise it is simply not a circumference (distance around a closed curve).

Again Doron your focus is on the infinite activity of adding the fractional values, your old infinite list can not be completed dodge. One does not need to perform an infinite number of additions to show that an infinite convergent series has a finite sum, as already demonstrated.

In fact if the infinite series of additions can not be completed by you then the infinite series of multiplications can not be completed by you either. Thus your claim of “It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2” is false by your own assertions of your own limitations. Just as before, the continuing infinite activity you depend upon to keep you from reaching the limit 1 also prevents you from changing that limit to 2 by an infinite series of multiplications, which are actually just an infinite series of additions (each fractional value added to itself). You can’t have it both ways Doron, the requirement for an infinite series of additions prevents you from reaching the limit but the requirement for an infinite series of additions does not prevent you from changing the limit from 1 to 2.

Since the basic mathematical principles used in the self similarity proof are that 1/2+1/4+1/8+1/16… = 1/2+1/4+1/8+1/16... and 1/2+1/4+1/8+1/16… + 1/2+1/4+1/8+1/16… - (1/2+1/4+1/8+1/16…) = 1/2+1/4+1/8+1/16…. You are going have to prove one of those fundamental mathematical relationships to be wrong. Again this is very simple and basic math. That you seem to have such a demonstrative problem with it simply confirms that you just do not comprehend mathematics. You simply assuming “we did not reach the limit value 1” does not constitute proof that “we did not reach the limit value 1”. Just as you simply claiming “now we simply do not reach the limit value 2” based on your simple assumption that “we did not reach the limit value 1” does not constitute proof of anything other than you like to make assumptions and claim they are valid, without any proof.
 
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doronshadmi said:
Is there a particular reason of why do you continue to ignore, for example, http://www.scribd.com/doc/17039028/OMDP , http://www.scribd.com/doc/21967511/...considerations-of-Some-Mathematical-Paradigms or

[qimg]http://farm5.static.flickr.com/4047/4390093906_6c3ae0ab88_o.jpg[/qimg]
[qimg]http://farm5.static.flickr.com/4006/4389327007_f968923c21_o.jpg[/qimg]
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I want to see the circumstance when a number is used qualitative relationally, as opposed to the usual local only, element, quantity. In your little paper cited above, it's clear that numbers are being used to quantitave ends.

At best what I'm getting from this is that a number can be used notationally or nominatively (instead of merely cardinaly and ordinaly). A number can be used as a marker of a bead idependent of the count of beads.

Perhaps more qualitatively, a number an be used adjectivally to code the degree of some quality.
For example a color code that identifies the degree of hue.
In this particular context, there is a meaning to the addition of hue 3 and hue 2. There is a resulting lightening or darkening of hue to another code value.
So numbers in certain contexts can be used to identify value.
This is a qualitative/relational/symbolic use of number.
Of course ordinary language does this frequently.

But I take it that's not much of what you want to make of it.

Sure, without a memory/object interaction in which I remember both the beads I've counted as opposed to the beads I haven't, and the count so far, I can't count or come to a definite sum. And yes we need to be aware of the individual item included in the count.
But this is too obvious and general a point to be an applied application.

A. How do I ballance my need for an income with right livelihood and my desire to have creative employment?
B. Simple! It's a memory/object interaction!

But I think your point is something more like this:
If I'm thinking in a non-linear fashion, I won't be bound to a step by step counting process but will see the wider view of non-linear associations.
If I stop to smell the roses, I'll find a complex of associations and associative pathways I've ignored and within that a novel solution.

We all do this in the process of solving problems more difficult than quantity calculation.
I'm not sure that stoping each time I do addition to note all the possible this one was coiunted-this one wasn't combos, is going to raise my awareness very much.

As I've said before, the key ethical essence isn't in how I count objects, but in how I regard persons.

But if your turning of simple arithmatic into a complex noting all ther possible configurations of of what was and what wasn't remembered as counted, helps you be aware that you are an active person and not a mere calculating machine, I cannot deny you the value of your ritual.
 
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You're also saying, it seems, that conventional math "leaps" to and deals only with situations where quantity and order are defined and clearly known.
But your ONs include the situations where there is an ambiguity or the sums aren't simply clear and are uncertain.

I would not call such a circumstance a matter of quality as opposed to quantity.
It's merely uncertain quantity of objects. (Because of uncertainty enetered into the count.)
And a quantity held in memory is a quantity not a quality.
(Yes, I know the number is quantity and quality because they are generated by the Quality/Quantity Interaction. But what is the actual use you are making of it?)

What it seems you are calling for is a way of seeing in which numbers aren't signify more value than just the price tag at Wal-mart. Number must exhibit an ethical dimension and have an ontological meaning.

Ordinarity, a combo of qualtative and quantitative uses of number would look something like this:
We'd talk about a quality 3 DVD collection of the 3 Lord of The Rings movies.

A problem that arrises again and again in all this is that non-locality and quality are not synonomus concepts and don't fit together like peas in a pod.
I do equivocation in trying to make something coherent out of what you are saying, but you are doing a great deal of equivocation yourself.
We both should stop and smell the roses and the complexity we siumplify away.
 
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The Man said:
Doron, again if you are asserting a circumference you are asserting that limit (the circumference) is being reached.
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Only by a finite amount of steps.


I see that you still do not get the invalid result of (∞*(1/∞)=∞*0) = (1=0), which is the result of your ill reasoning.


The Man said:
In fact if the infinite series of additions can not be completed by you then the infinite series of multiplications can not be completed by you either. Thus your claim of “It can easily shown that if a circumference of length 1 is multiplied by 2, we get a circumference of length 2” is false by your own assertions of your own limitations.
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In fact you don't get that 1 or 2 are finite values, that are reached only by finite steps.

The Man said:
Already conclusively demonstrated to be false for a convergent infinite series some 2,300 years ago.
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Not even in your dreams.

wiki said:
http://en.wikipedia.org/wiki/Geometric_series#Sum

The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant.
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This constant (which is > 0) is exactly the reason that prevents from some geometric series to reach the value of a given limit.
 
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doronshadmi said:
I see that you still do not get the invalid result of (∞*(1/∞)=∞*0) = (1=0), which is the result of your ill reasoning.
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Why do you continue to trot out this same example and claim that it is by our "ill reasoning" that the inconsistency occurs? I don't get that result. It is only by disregarding actual Mathematics that you get the silly result. It is just your ill reasoning that continues to produce this invalid result.
 
Apathia said:
But this is too obvious and general a point to be an applied application.
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Nothing is obvious at the moment that you are opened to the infinite complexity that is based on Non-locality\Locality linkage.

Apathia said:
As I've said before, the key ethical essence isn't in how I count objects, but in how I regard persons.
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EDIT:

By OM you develop your ability to cherish the inflation's-free value non-trivial result of the interaction between the simple and the complex, known as personality, where this personality has a unique knowledge of the researched, which helps each personality (the same and also other personality) to be developed beyond any limited dogma of a given realm (abstract or not).

Apathia said:
And a quantity held in memory is a quantity not a quality.
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You still miss it.

A quantity is the result of the linkage of different qualities known by OM as Non-locality and Locality.

The quantitative result can be accurate or not, but is does not change the fact about the qualitative foundation of Quantity.
 
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doronshadmi said:
By OM you develop your ability to cherish the inflation's-free value the non-trivial result of the interaction between the simple and the complex, known personality, where this personality has a unique knowledge of the researched, which helps each personality to be developed beyond any limited dogma of a given realm (abstract or not).
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Waiter! I ordered Waldorf, not Word.
 
jsfisher said:
Why do you continue to trot out this same example and claim that it is by our "ill reasoning" that the inconsistency occurs? I don't get that result. It is only by disregarding actual Mathematics that you get the silly result. It is just your ill reasoning that continues to produce this invalid result.
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jsfisher, I see that you do not comprehend the size of each element that is based on 2^∞ cardinality (the cardinality of the continuum by your own paradigm) along a given infinite series of distinct values.
 
doronshadmi said:
Only by a finite amount of steps.
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So then you are simply not talking about an infinite series and your assertions are irrelevant in that regard, by your own assertion above


doronshadmi said:
I see that you still do not get the invalid result of (∞*(1/∞)=∞*0) = (1=0), which is the result of your ill reasoning.
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I see you are still trying to posit your own deliberately “invalid result” of your own “ill reasoning” onto others.


doronshadmi said:
In fact you don't get that 1 or 2 are finite values, that are reached only by finite steps.
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Again conclusively demonstrated as false some 2,300 years ago, again your simple assumptions do not constitute facts or proof.
 
wiki said:
http://en.wikipedia.org/wiki/Geometric_series#Sum

The terms of a geometric series form a geometric progression, meaning that the ratio of successive terms in the series is constant.
Click to expand...
This constant (which is > 0) is exactly the reason that prevents from some geometric series to reach the value of a given limit.

And likw jsfisher, you also do not comprehend the size of each element that is based on 2^∞ cardinality (the cardinality of the continuum by your own paradigm) along a given infinite series of distinct values.
 
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doronshadmi said:
jsfisher, I see that you do not comprehend the size of each element that is based on 2^∞ cardinality (the cardinality of the continuum by your own paradigm) along a given infinite series of distinct values.
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That has nothing to do with my question to you. Care to try again?
 
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