Deeper than primes

[dlorde]

You need to be bilnd in order to not see that this is not a pop-psychology, for example: http://en.wikipedia.org/wiki/Cerebral_hemisphere .

Oh good grief did you actually read that article?

It says:

Broad generalizations are often made in popular psychology about certain function (eg. logic, creativity) being lateralised, that is, located in the right or left side of the brain. These ideas need to be treated carefully because the popular lateralizations are often distributed across both sides.

Nuff said.

 

[doronshadmi]

Oh good grief did you actually read that article?

It says:



Nuff said.

I agree with this, both sides have to complement each other in order to understand things from more than one alternative.

In order to do that one enables to deal with the very existence of things that may be describabed in more than a one way.

This is how creativity is expressed and enables one to use some system in more than one way , and my view of Cardinality is some example of how this approach works.

We can decide that that Cardinality is the number of different things that belong to some set, and then we compare between sets and define the difference (if exist) between them, and then build a theory that is based on this kind of measurement.

But we also take the same objects and include in our research the difference between the investigated members that belong to some set.

By doing this we do not ignore the complexity of the investigated objects, starting from each member of the set and include this complexity on the entire measured set .

By doing this we get a much more wider realm that enables to understand better any chosen partial measurement of it, exactly because now we are aware of our decision to measure only a partial case of the wider case.

The difference be between the wider and the partial cases of X is in my opinion the best way to understand and use X for our purpose.

For example, the rules of the Chess game are non-local w.r.t any particular game but they are actually expressed by many different concrete games, where each game is some local manifestation of these rules.

By using this analogy we can learn that complex systems are actually a linkage between simple fundamental terms or rules that are rich enough to be expressed in many different ways that still express that same simple rules.

The idea of OM is to take the non-locality of the rules and the locality of the many different expressions of the rules and look as this rule\expression linkage as a generalization of the researched realm.

We can choose any part of that realm and use it for our purpose, but now we are doing it according to a wider understanding, that can help us to understand better our partial reseach.

This is the idea of Complexity as a guidance of any research, which enables us to develop the whole\parts needed sensitivity in order to deal with non-trivial systems that enables interdisciplinary and specific knowledge under a one comprehensive framework.

If the mathematical science will use both interdisciplinary and specific methods in order to enrich its body of knowledge, I think that all of us will enjoy the fruits of this approach.

In my opinion, our brain is a living example of a system that was develop during the years according to the principles of Complexity, where simple (non-local) rules manifests themselves in many expressions that seeking for the methods that help them find the balance during their different local expressions, and in my opinion it is a fruitful approach that may help us to find the balance between Ethics and Logics as two manifestations of a one complex system, our brain\body system.

OM seeks to develop the synergy between Ethics and Logic, by using the understanding of the synergy principles of our brain\body system while it works in the word.

What do you think? (and please take in a account that we are in a philosophical forum).

 

[doronshadmi]

Again is that your direct perception that told you cardinality was ‘a measurement unit of existence’ and that an empty set “is an existing thing but its Cardinality = 0.”? Your direct perception does not appear to measure up when it comes to your own ascription of ‘a measurement unit of existence’

The cardinality of the existence of the empty set is ∞ exactly as the existence of an empty stage.

0 is the cardinality of existence of the players on this stage.

In both cases cardinality is used to measure the existence of things.

The same thing holds in a non-empty set. Also in this case the cardinality of the existence of the non-empty set is ∞, where any non-0 cardinality is used to measure the existence of the players on the stage.

You can measure the complexity of the players or on not, is it up to you, but in both cases (empty is non-empty set) the existence of the stage is independent of the existence of the players.

 

[The Man]

The cardinality of the existence of the empty set is ∞ exactly as the existence of an empty stage.

0 is the cardinality of existence of the players on this stage.

In both cases cardinality is used to measure the existence of things.

The same thing holds in a non-empty set. Also in this case the cardinality of the existence of the non-empty set is ∞, where any non-0 cardinality is used to measure the existence of the players on the stage.

You can measure the complexity of the players or on not, is it up to you, but in both cases (empty is non-empty set) the existence of the stage is independent of the existence of the players.

After more then three days that is the best you can do?

Let’s try it…

With

“The cardinality of the existence of the empty set is ∞”

and

“any non-0 cardinality is used to measure the existence of the players on the stage.” for “a non-empty set”.

Thus for a set containing only the empty set, the empty set is that ‘player on the stage’ and it’s ‘cardinality of existence’ is “∞” so the “non-0 cardinality” that “is used to measure the existence of the players on the stage” for this set containing only the empty set is “∞”. However the actual cardinality of a set that contains only the empty set is simply 1.

Let’s try it a different way Set A is {1} having a cardinality of 1. Set B contains only set A thus set A is that ‘player on the stage’ for B. Set A is a “non-empty set” and thus its ‘cardinality of existence’ is “∞” and so the “non-0 cardinality” of set B as “the existence of the players on the stage” of B is ‘cardinality of existence’ of A or “∞”.

Again you simply can not seem to decide (or directly perceive yourself) what exactly your “cardinality of the existence” is suppose to represent.


I would have recommended that you might have been better off had you taken three more days before you replied, but seeing as how the past twenty years (by your own claims) has done little to help you, I doubt with an extra three days that you would have done any better.

 

[dlorde]

OM seeks to develop the synergy between Ethics and Logic, by using the understanding of the synergy principles of our brain\body system while it works in the word.

What do you think? (and please take in a account that we are in a philosophical forum).

I see where you're coming from, and I think that, as you just expressed it, it is wholly laudable, but I just don't see that OM, however well intentioned, will have any impact at all in that respect. I think we all understand what it is trying to achieve, but almost no-one (here) who has tried to follow the argument thinks it is a rational system. You yourself admit that no-one else 'gets' it.

In fact, I think that intelligent, broad-minded people who have gained or are gaining expertise in some area of knowledge or performance, will bring wider concerns to bear on their speciality as their competence encompasses the use of seemingly unconnected metaphors and analogies extending into the larger society and environment. They start thinking about their subject and it's relationships in more generic terms, and this will naturally bring a moral and ethical dimension into their speciality. There are some prerequisites for this kind of developmental flowering within expertise, including a wide-ranging basic education encouraging freedom of thought.

In my opinion, the key to opening minds to wider moral and ethical concerns is not the introduction of new techniques and fashionable systems, but to ensure that the basic quality and freedom of early education is maintained and enhanced, so students get a chance to discover the options and paths available and experience the pleasure of the pursuit of knowledge that suits their personalities and abilities.

Research has shown that almost any competent individual can gain expertise in an area of knowledge, given around 10,000 hours of practice, but to make that kind of commitment requires an abiding interest in the subject and a supportive environment. Not everyone will take such a high road, but a good basic education and a supportive environment will help them to make an informed choice.

 

[doronshadmi]

Thus for a set containing only the empty set, the empty set is that ‘player on the stage’ and it’s ‘cardinality of existence’ is “∞”

No, the cardinality of the existence of Set (empty or not) is ∞ , and it is the stage of any possible collection of players.

You simply do not agree with the notion that Cardinality is the measurement of the existence of things.

In that case you miss the whole idea of Complexity and limit your self to the first level of the existence of the players on the stage, but this is your limitation, not mine, and by your limitation you do not talk about my new viewpoint about the concept of Cardinality.

It has to be noticed that ∞ has no successor exactly as 0 has no predecessor.

The cardinality of the players is x such that 0 < x < ∞ , and you ignore this viewpoint about cardinality.

Again, this is a philosophy forum, where new fundamental ideas are born, and you The Man simply stick to the old ideas, that’s all.

 

[doronshadmi]

I see where you're coming from, and I think that, as you just expressed it, it is wholly laudable, but I just don't see that OM, however well intentioned, will have any impact at all in that respect. I think we all understand what it is trying to achieve, but almost no-one (here) who has tried to follow the argument thinks it is a rational system. You yourself admit that no-one else 'gets' it.

In fact, I think that intelligent, broad-minded people who have gained or are gaining expertise in some area of knowledge or performance, will bring wider concerns to bear on their speciality as their competence encompasses the use of seemingly unconnected metaphors and analogies extending into the larger society and environment. They start thinking about their subject and it's relationships in more generic terms, and this will naturally bring a moral and ethical dimension into their speciality. There are some prerequisites for this kind of developmental flowering within expertise, including a wide-ranging basic education encouraging freedom of thought.

In my opinion, the key to opening minds to wider moral and ethical concerns is not the introduction of new techniques and fashionable systems, but to ensure that the basic quality and freedom of early education is maintained and enhanced, so students get a chance to discover the options and paths available and experience the pleasure of the pursuit of knowledge that suits their personalities and abilities.

Research has shown that almost any competent individual can gain expertise in an area of knowledge, given around 10,000 hours of practice, but to make that kind of commitment requires an abiding interest in the subject and a supportive environment. Not everyone will take such a high road, but a good basic education and a supportive environment will help them to make an informed choice.

I am talking about the simplest state of mind of getting knowledge by using direct perception. On top of this simplest state of mind one can develop any complex body of knowledge where both Ethics and Logics are complements simply because both of them are derived from the simplest state of mind.

In order to see where I am coming from you have to be directly aware of the simplest state of mind, which is the basis of any mental activity, whether it is Ethical or Logical.

 

[The Man]

No, the cardinality of the existence of Set (empty or not) is ∞ , and it is the stage of any possible collection of players.

So you first say “No” then proceed to confirm exactly what I said and you quoted.

You simply do not agree with the notion that Cardinality is the measurement of the existence of things.

Because it is not and you simply do not agree with yourself about what “existence” or “things” you want to ‘measure’.

In that case you miss the whole idea of Complexity and limit your self to the first level of the existence of the players of the stage,

Your assumption of such limitation is simply wrong and as far as your notion of “Complexity” goes I have no doubts that it is as convoluted, undefined, circular, self contradictory and useless as your other notions have clearly demonstrated.

but this is your limitation, not mine, and by your limitation you do not talk about my new viewpoint about the concept of Cardinality.

I have done nothing but talk about it and lately specifically that you simply can not make up you mind what “existence” or “things” you want your “measurement of the existence of things” to, well, ‘measure’. Also your “viewpoint about the concept of Cardinality” has nothing to do with the concept of cardinality in spite of your continued insistence on the misuse of that word.

It has to be noticed that ∞ has no successor exactly as 0 has no predecessor.

It has to be noted that -1 is a predecessor of 0 in both the real numbers and the integers. If you wish to limit the set you are considering to only the natural numbers then it is you who is limiting the “complexity” of your notion of “measurement of the existence of things”.

The cardinality of the players is x such that 0 < x < ∞ , and you ignore this viewpoint about cardinality.

I have not ignored it specifically because it is not “about cardinality” by any meaningful use of that word.

Again, this is a philosophy forum, where new fundamental ideas are born, and you The Man simply stick to the old ideas, that’s all.

Philosophical crap is still crap Doron, you have just been wallowing in it for so long that you have become accustom to the stench.

Two weeks (or a fortnight) for this response, I would recommend that you try to take more time and think things through, but doubt it would make any difference in your responses.

 

[doronshadmi]

So you first say “No” then proceed to confirm exactly what I said and you quoted.

Let us show your crap again:

Thus for a set containing only the empty set, the empty set is that ‘player on the stage’ and it’s ‘cardinality of existence’ is “∞”

The existing stage has cardinality ∞.

A player has cardinality x, such that 0 < x < ∞.

If the empty set is considered as a player on the stage, that its cardinality is 1.

You simply do not distinguish between |{}| = ∞= the cardinality of the stage that is notated by the outer "{""}", and the cardinality of the player of {{}} that is = 1 and notated by the inner "{""}".

In general, you do not get the independent existence of the stage and the independent existence of the players.

If linked then the stage is non-local w.r.t the players and the players are local w.r.t the stage.

This simple and profound beauty is beyond your limited serial-only first-level-only measurement of players-only, where the stage is used as your hidden-assumption, whether you like it, or not (without it you simply unable to collect players).

The Man your abstract ability is limited, and this is a trivial fact.

As about time gaps, I have more important things to do beside to answer to your limited crap.

 

[The Man]

Let us show your crap again:


The existing stage has cardinality ∞.

A player has cardinality x, such that 0 < x < ∞.

If the empty set is considered as a player on the stage, that its cardinality is 1.

Nope once again you’re simply misusing the word cardinality. If you want to make up you own concept then make up you own word to identify it.

You simply do not distinguish between |{}| = ∞= the cardinality of the stage that is notated by the outer "{""}", and the cardinality of the player of {{}} that is = 1 and notated by the inner "{""}".

No I simply distinguish the actual, established and well defined concept of cardinality from whatever inconsistent fantasy you are attempting to hijack that word for.

In general, you do not get the independent existence of the stage and the independent existence of the players.

If linked then the stage is non-local w.r.t the players and the players are local w.r.t the stage.

This simple and profound beauty is beyond your limited serial-only first-level-only measurement of players-only, where the stage is used as your hidden-assumption, whether you like it, or not (without it you simply unable to collect players).

Well if you are “simply unable to collect players” without your “stage” then they aren’t independent. The existence of your “players” is, by your own assertion, explicitly dependent on the existence of your “stage”. Still can’t get around that self contradiction thing can you?

The Man your abstract ability is limited, and this is a trivial fact.

As about time gaps, I have more important things to do beside to answer to your limited crap.

Well then by all means, please, continue to do your “important things”, as your assertions and arguments have certainly gotten no better. It still simply amounts to you proclaiming we should accept whatever you say or we are simply “limited”. Take as much time as you like, I can assure you I will still be here to throw whatever crap you tout right back at you.

 

[doronshadmi]

No, I simply distinguish the actual, established and well defined concept of cardinality from whatever inconsistent fantasy you are attempting to hijack that word for.

No, you simply stacked by the current agreement of Cardinality that prevents from you to see the wider picture of this concept, which is not limited to the first-level of existence of the players on the stage.

Your “established and well defined concept of cardinality” is nothing but a partial case of Complexity’s understanding, and as a result the rest of your framework suffers from this serial-only partial understanding of the existence of Complexity and Complexity’s measurement.

You simply afraid to think out of the box The Man, and this fear is clearly seen all along this thread.

Well if you are “simply unable to collect players” without your “stage” then they aren’t independent.

No The Man, you simply unable to get Connectivity and Isolation as independent existence that if linked are understood as non-locality and locality aspects of a one framework.

The player is isolated by default and the stage is connected by default.

When Connectivity and Isolation are linked, then and only then Cardinality beyond 0 is possible (think about a stage with more than 0 players on it).

Isolation on its own cannot be counted unless it is a player on the stage, and Connectivity on its own has cardinality that has no successor, notated as ∞, such that Cardinality x is 0 < x < ∞.

Without totalities like "that has no successor" and "that has no predecessor" you have no consistent framework of Complex existence in the first place, and Complexity is exactly the result of the linkage between that has 0 cardinality and that has ∞ cardinality, such that cardinality x refers to complex and non-total existence.

Some examples:

{} is exactly the total existence that has ∞ Cardinality on one hand and 0 Cardinality on the other hand.
The players’ existence is between these totalities and measured by x (0 < x < ∞).

The first and minimal thing that has x cardinality is the empty set as a player on the stage, notated as {{}}.

 

[doronshadmi]

Continue:

By following the notion of Complexity x cardinality is not limited to the first-level of the measured complexity (cardinality ∞ and 0 are not added to x when x measures some complexity, for example: |{{}}| = 1 exactly because x cardinality of the inner “{“”}” is 1 where 0 (the cardinality of the content of the inner “{“”}” ) and ∞ (the cardinality of the outer “{“”}”) are not added to x, since they are totalities.)

So we have the first non-total existence that has cardinality 1, where ∞ is the cardinality of the existence that enables isolade players to be gathered beyond their isolated 1 cardinality and noting (0 cardinality) enables to save the independence of the non-total existence of that has cardinality x from the total existence of that has cardinality ∞.

I can assure you I will still be here to throw whatever crap you tout right back at you.

All you do is to throw your crap within you own playground, because you did not get yet out of your box in order to really get OM.

 

[zooterkin]

{} is exactly the total existence that has ∞ Cardinality on one hand and 0 Cardinality on the other hand.

{} has two hands?

 

[doronshadmi]

{} has two hands?

1) Cardinality is the measurement unit of the existence of a thing.
2) Non-local Atom is an existing thing (has cardinality ∞) that has no sub-exiting thing(s) (has cardinality 0).
3) Any non-atomic thing is a complex that has cardinality x such that 0 < x < ∞ .
4) The non-local atom is called the stage and any complex is called a player, where a player that does not have sub-existing things, is called a local atom.
5) Players are gathered into complexities by the ∞ aspect of the non-local atomic state, and each player is independent of the ∞ non-local atomic state by the 0 aspect of the non-local atomic state, exactly because the non-local atomic state has no sub-existing things (the players are on the stage and not parts of the stage). As a result no gathered collection of players has the cardinality of existence of the non-local atomic state because any given x has cardinality 0 < x < ∞, which is the property of a non-atomic state or a local atomic state.

Standard Math has no understanding of the atomic state (non-local or local) and the complexities of the non-atomic states, which are derived from the opposite and total cardinalities of the non-local atomic state.

Furthermore, Standard Math has no understanding of the generalization of the atomic state as an existing thing that has no sub-existing things.

 

[jsfisher]

*yawn*

 

[The Man]

<Preceding nonsense snipped>

{} is exactly the total existence that has ∞ Cardinality on one hand and 0 Cardinality on the other hand.

<Subsequent nonsense snipped>

Once again you show that you simply can not make up you mind what “things” or “existence” you want your “measurement of the existence of things” to, well, ‘measure’

 

[doronshadmi]

Once again you show that you simply can not make up you mind what “things” or “existence” you want your “measurement of the existence of things” to, well, ‘measure’

Once again you can't get the existence of the atomic state, which is an existing thing that has no sub-existing things.

Complexity is derived from the linkage between two types of the atomic state, which are:

1) The non-local type is notated by the outer “{“”}”, and its cardinality is ∞, where the cardinality of its sub-things is 0.

2) The local type is notated by the inner “{“”}” of the expression {{}}, and its cardinality is 1, where the cardinality of its sub-things is 0.

Based on the link between the non-local and the local types of the atomic state, one defines the Cardinality of the Complexity of some form, where the cardinality of Complexity is non-total and notated by x such that 0 < x < ∞.

By using this approach one can choose if he wishes to measure the Cardinality of some complex (for example: |{{{}}}|=2)
or not (for example |{{{}}}|=1, and in this case only the first level of the complex is considered).

OM’s approach about the fundamental forms is comprehensive and enables to deal with Complexity by giving the mathematician the ability to tune complexity as needed.

This flexibility is avoided by Standard Math because it does not deal with the researched things from their level of existence.

The Man, http://www.internationalskeptics.com/forums/showpost.php?p=5107575&postcount=5974 is beyond your abstraction ability.

Also you did not deal with http://www.internationalskeptics.com/forums/showpost.php?p=5046125&postcount=5944 and you did not answer to the two questions at the end of this post.

 

[doronshadmi]

It has to be noted that -1 is a predecessor of 0 in both the real numbers and the integers. If you wish to limit the set you are considering to only the natural numbers then it is you who is limiting the “complexity” of your notion of “measurement of the existence of things”.

It has to be noted that Cardinality cannot be negative because it measures the existence of things, where the minimal measurement of existence is 0 (the measurement of non-existence).

 

[The Man]

<preceding nonsense snipped>
By using this approach one can choose if he wishes to measure the Cardinality of some complex (for example: |{{{}}}|=2)
or not (for example |{{{}}}|=1, and in this case only the first level of the complex is considered).

Once again you misrepresent the notion of Cardinality and simply demonstrate that you can not make up you mind what you want your “measurement of existence” to ‘measure’.

<other preceding nonsense snipped>

Also you did not deal with http://www.internationalskeptics.com/forums/showpost.php?p=5046125&postcount=5944 and you did not answer to the two questions at the end of this post.

I did in fact respond directly to that post and until you can establish what you specifically mean by “existence” or “exists” your questions simply remain without meaning.

It has to be noted that Cardinality cannot be negative because it measures the existence of things, where the minimal measurement of existence is 0 (the measurement of non-existence).

No “Cardinality cannot be negative because” one simply can’t define a set where the members of that set are missing or, in other words, are not members of that set. That you choose to restrict your “measurement of existence” to the natural numbers does not make Cardinality your “measurement of existence” nor does it make your “measurement of existence” Cardinality, it simply restricts both to the same set of values, the natural numbers.

 

[XxDeadlyNinjaxX]

This Thread is HUGE.