The power of the transfinite system

[Organic]

Hi,



First, please look at this example (It takes about 1 minute to load it) :

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


From this example we can understand that if aleph0 is related to all N members then any n of n^aleph0 cannot be but 0.

The reason is very simple: When we deal with all N members, the power of |N| (=aleph0) is too strong for any information structure, which is constructed on some n>0 base.

Shortly speaking, the "rainbow of information" does not exist when we reach the power of aleph0.

No information --> no input --> no results --> no conclusions.

Therefore transfinite universes, which constructed on ...2^(2^(2^aleph0))... does not hold.

When we try to force the transfinite idea on any information system (including Math language) we get:

...2^(2^(0^aleph0))... = 1 = {__} = Fullness.

XOR

...0^(0^(0^aleph0))... = 0 = {} = Emptiness


{} XOR {__} contents are actual infinity and cannot be reached by any information system (including Math).


Organic

 

[Hurkyl]

But {__} has been reached by your system, thus your system cannot have any information in it! (Otherwise it would be an information system, right?)

 

[Organic]

No {} and {__} are the unreachable limits of the open interval ({},{__}).

please read again this paper and its links:

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

Again:

{} is only an x-model of the content Emptyness.

{__} is only an x-model of the content Fullness.

Please look here:

http://www.geocities.com/complementarytheory/CATpage.html

and then read the Major Theorem.

Yours,

Organic

 

[master_coda]

Since your system can describe {___} it clearly reaches it. Thus we have two possiblities:

1. Your system contains no information.
2. {___} is not in fact unreachable by an information system.

Unless by "reach" you mean something else. But if we can describe something, we don't really care about anything else.

 

[Organic]

Dear master_coda,

You wrote:

...if we can describe something, we don't really care about anything else.

By your comment you do not distinguish between x-model and x-itself.

The set idea cannot be but an x-model, therefore {} is an x-model of Emptiness and {__} is an x-model of Fullness.

Any description is only an x-model, for example: any description of silence is not silence itself.

This is my Major Theorem before I starting to develop any theory.

Again, no theory is x-itself but only an x-model.

If you don't understand or don’t agree with that then we cannot communicate in this subject.

My point of view can be found here:

http://www.geocities.com/complementarytheory/CATpage.html

 

[master_coda]

So model of information cannot contain any information itself.

Likewise, any model of logic cannot contain any logic itself. Thus we cannot use logic to talk about logic.

Of course I cannot agree with that.

 

[matt grime]

At Organic's request, here are some comments on his material:





>http://www.geocities.com/complementarytheory/PTree.pdf

Pretty, but as with most of the articles there unclear.

>From this example we can understand that if aleph0 is related to all N members then any >n in n^aleph0 cannot be but 0.

How or why can one understand this? The article has an unmotivated picture with some interpretation that is not explained clearly. and what does 'n in n^aleph-0' mean? 'in' would usually indicate some kind of set were being talked about.


>The reason is very simple: When we deal with all N members, the power of |N| >(=aleph0) is too strong for any information structure, which is constructed on some n>0 >base.

what does it mean for something to be 'too strong for any information structure' and for that matter, what is an information structure?

>Shortly speaking, the "rainbow of information" does not exist when we reach the power >of aleph0.

More undefined terms. And as with a lot of problems people seem to have with infinity, how does on reach the power of aleph0. There is (reasonably explicitly) some presumption that one 'travels' towards infinity, but because one never reaches it thus having all these inherent contradictions in mathematics. Often it is to do with constructibility and Turing Machines and the issues of finitely many steps.

>No information --> no input --> no results --> no conclusions.

>Therefore transfinite universes, which constructed on ...2^(2^(2^aleph0))... does not >hold.

Obviously wrong.

>When we try to force the transfinite idea on any information system (including Math l>anguage) we get:

>...2^(2^(0^aleph0))... = 1 = {__} = Fullness.

Ok. the left hand side of that is an infinite cardinal I think, though I'm not sure what 0^aleph0 is, the next term is a finite cardinal, the next is something that we must interpret as a set, though which one is never explained, the last is a word. Do you not think that '=' is the wrong symbol to use here?

>XOR

>...0^(0^(0^aleph0))... = 0 = {} = Emptiness

I think ditto is a valid comment


>{} XOR {__} contents are actual infinity and cannot be reached by any information >system (including Math).


>Organic

Matt

 

[Organic]

Some correction:

I wrote:

...2^(2^(0^aleph0))... = 1 = {__} = Fullness.

XOR

...0^(0^(0^aleph0))... = 0 = {} = Emptiness

----------------------------------------------------------------------------

Instead, it has to be:

...0^(0^(0^aleph0))... = 1 = {__} = Fullness.

the second one ...2^(2^(0^aleph0))... = the "never ending" tree:

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

 

[Organic]

Master_coda,

You are going too far with your conclusions.

We can talk about anything in any form, depth or direction but always we have not to forget that any theory about something is never the something. that's all, nothing less, nothing more.

Logic is the simplest form of some x-model, if it was x then and only then it was beyond our power to deal with it.

Shortly speaking, we can deal and develop any form of x-model, and Complementary Logic is a good example for this.

And why it is a good example?

Because first of all it is aware to its limitations as an x-model.

 

[master_coda]

But the only reason your "theory" is aware of its limitations is because you've made up limitations. You haven't shown what the limits in fact are, you've just said "there are limits, and I'm making up words like emptiness and fullness to describe them".

 

[Organic]

Hi matt grime,

Where is your imagination?

Do you really cannot imagine that no tree of any base can carry the power of aleph0 and survive?

Again, no information can be used as input when we reach actual infinity.

 

[master_coda]

Organic, why do you keep using the term "aleph0"? You don't agree with any of the mathematics behind it, and you don't use it in any way resembling it's actual definition.

 

[Organic]

Aleph0 = {__} through my point of view.

If i want to make a mutation in this concept, i have no choice but to show my new interpretation to aleph0.

Therefore ({},{__}) = ({},aleph0).


More than that, any concept in x-model can be changed by its meaning.

 

[master_coda]

Whats the point of calling it aleph0 if you don't have aleph1, aleph2, etc. ?

Any concept in any model can be changed.

 

[Organic]

First I like the name because my language is hebrew and aleph is the first leter in my alpha-beth.

Also through my point of view aleph0 has exactly 0 points, and this is the reason why aleph0 = {___} where ___ has 0 points.

But I'll be glad to know what name to you want to give to {__}.

 

[master_coda]

Call it {___}. At least that'll help avoid equivocation.

 

[Organic]

Thank you Master_coda, I'll call it Full set (which is the opposite of Empty set).

 

[matt grime]

Originally posted by Organic
Hi matt grime,

Where is your imagination?

Do you really cannot imagine that no tree of any base can carry the power of aleph0 and survive?

Again, no information can be used as input when we reach actual infinity.

What the hell as imagination got to do with it? I can imagine lots of things that are false, it doesn't mean I call them mathematics.

Again you are talking about reaching infinity. This demonstrates you don't understand what infinity means. Which infinity? The infinity of [0,oo)? there is no such point. One doesn't reach it. The north pole in the standard one point compactification of the complex plane?

 

[Organic]

Matt,

Please look at the white arcs in: http://www.geocities.com/complementarytheory/PTree.pdf

When we reach aleph0, they are gone (become a one solid line {___}, and base=0 ).

Without them there is no information to deal with.

More than that, {___} content is too strong to be measured by 1-1 map.

Please also look at: http://www.geocities.com/complementarytheory/RiemannsLimits.pdf

Thank you,

Orgainc

 

[matt grime]

Originally posted by Organic
Matt,

Please look at the white arcs in: http://www.geocities.com/complementarytheory/PTree.pdf

When we reach aleph0, they are gone (become a one solid line {___}, and base=0 ).

Without them there is no information to deal with.

More than that, {___} content is too strong to be measured by 1-1 map.

Please also look at: http://www.geocities.com/complementarytheory/RiemannsLimits.pdf

Thank you,

Orgainc

How hard is it to understand that one does not physically 'reach aleph-0'. It is not a point in space, it is not even a limit point of physical space. It is the cardinality of the Natural numbers.

Further, a picture is not a proof, just because you can't draw infinitely divisible objects does not mean mathematically that after a finite number of steps repeatedly dividing by two gives you zero, for instance.

Please stop misusing mathematical ideas and claiming they are still mathematical.

What for instance does it mean to be measured by a 1-1 map? measured on what scale? Measured by what means?

You've ignored the question again about what it means to be too strong to be measured. In fact you ignore anything you can't explain, which is pretty much every criticism laid at your door. Define this term. Go on, just define it, here in this forum, and not by posting some unrelated pdf file.

 

[Organic]

Matt Grime,

My pictures don’t have any connections to physical sizes, they are rigorous exactly like any definition that expressed by notations.

One thing is for sure, you don’t have the ability to translate them to abstract thoughts.

Notations, pictures, and so on are only tools that help us to organize our ideas.

These pictures are rigorous because they are based on Complementary Logic:

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



But your problem is deeper then that, you do not distinguish between x-model and x-itself, (where x is infinity) and I do distinguish between them.

Please read my main website’s page:

http://www.geocities.com/complementarytheory/CATpage.html

and also:

http://www.geocities.com/complementarytheory/X-model-X.pdf

If you don’t agree with my main theorem (after you read it), then there is no use to continue our communication on this subject.

Yours,

Orgainc

 

[matt grime]

Originally posted by Organic
Matt Grime,

My pictures don’t have any connections to physical sizes, they are rigorous exactly like any definition that expressed by notations.

One thing is for sure, you don’t have the ability to translate them to abstract thoughts.

Notations, pictures, and so on are only tools that help us to organize our ideas.

These pictures are rigorous because they are based on Complementary Logic:

http://www.geocities.com/complementarytheory/CATpage.html

HOwever it is you who is claiming that because, in the diagram, they all become indistinguishable that something is going on. So you are requiring a phyiscal realization.

But your problem is deeper then that, you do not distinguish between x-model and x-itself, (where x is infinity) and I do distinguish between them.

Please read my main website’s page and also:

http://www.geocities.com/complementarytheory/X-model-X.pdf

If you don’t agree with my main theorem (after you read it), then there is no use to continue our communication on this subject.

Yours,

Orgainc

You still haven't adequately defined your infinity, or its model. And you still keep posting pdfs that you know I will not read on principle.

 

[Organic]

If you don't read my major theorem about math by principle then this is my last reply to you.

 

[matt grime]

The main statement is

no model of x is x.

Where x is something you've to define at a later date?

Correct.

x is a theory, its model is a model, they are distinct, clearly not the same.

Do you also accept that a set and an inequality are not the same? And are therefore not equal?

Now, are you going to answer the challenge to clearly and unambiguously state what you mean by

'too strong to be measured'

in simple text and not via some unrelated pdf?

As a guide line:

define a 'measurement'.

define 'strength' of objects in terms of this measurement.

prove that there exist things with greater 'strength' than any given 'amount' or similar.

 

[Organic]

Matt,


It is very simple when you understand my point of view.

It is written here:

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

If you read it we will see that there are two types of one:

type 1) one of many (any object that belongs to some collection of finitely or infinitely many objects).

type 2) ONE (an infinitely long solid line that cannot be reached by type 1 objects).

1-1 map can be used only between type 1 objects.

When we use the words 'all' or 'complete' with some collection that include infinitely many objects, we get type 2 object.

I hope you understand that there cannot be any 1-1 map between type 1 and type 2.

Therefore the 1-1 map cannot be used if we force |N|(= aleph0) to be the cardinal of 'all' N infinitely many objects.

The main property of infinitely many type 1 objects is not to be completed, therefore we cannot talk on 'all' N objects.

A collection of sperated and distingushed infinitely many objects can exist if and only if we DO NOT have 'all' of them.

You will not uderstand this if you don't read, and (I hope)
try to understend what I write here:

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

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


Yours,

Organic

 

[matt grime]

So you aren't going to answer the question I asked?

I'll repeat it here:

Define precisely what it means for a set to be 'too strong to be measured'


As for your actual reply, I'm afraid I don't follow what you're attempting to do.

Please define 'one' of which there are two types. (thus making 'one' a bizarre choice of name for it).

Give examples of objects which are type 1 one and type 2 one.

And you still keep posting pdf links for me despite me asking you not to. It's almost as if you don't want me to read it.

 

[Organic]

Dear Matt,


My rigorous examples (my models) are based on pictures.

Your interpretation that math rigorous definitions and examples MUST be based on notations (otherwise it is not abstract) is wrong.

Notations, diagrams, pictures, and so on, are only tools that help us to organize our ideas in the most simple and rigorous ways.

I use pdf because this is the simplest way to combine graphical/textual information about some abstract and rigorous model.

I believe that you know the idiom: "One good picture = 1000 words".

Now, please look again at this pdf:

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

By using Riemann's ball as our model, we find that the top line has two results.



Result 1:

Infinitely many intersections with the middle-line, where each intersection is one of infinitely many intersections.

This universe of infinitely many intersections is what I call potential infinity.



Result 2:

The top line cannot intersect itself, and when oo-line is parallel to middle-line, then top line is the ONE, or what I call the actual infinity ( or the Full set {__} ).

 

[matt grime]

So you can't answer my question then? It is not in the scope of your theory to explain itself and be consistent?

A picture can be a useful tool for explaining something, it is not in itself worth anymore than that as it is realized in an imperfect system

Your Riemann Limit still insists that one must reach infinity, and that our number systems are limited to lying in certain regions. Do you know about the extend number systems that exist? Infinity is a useful point in the compactification of the Real Line or Complex Plane. You are misusing it to attempt to sa something about the non compact object.


"we find the top line has two results"

please rephrase that so it is coherent.


so this unattainable point at infinity is the total set {__}?


You genuinely believe this is worth something? Guess I'll just have to be one of those pesky scholastic sceptics. It's rapidly becoming apparent (ok, it always has been) that you have no intention of attempting to explain yourself clearly. Fine, these things seem only to be important to your understanding of something. I think there is a better way of thinking, but everyone must have there own view, and it is good that you at least think about these things. However, you are attempting to use these 'imaginations' to say that mathematics, with its boolean logic is flawed because it can't handle the infinity you pick. Well, mathematics doesn't share your opinion of infinity, or at least doesn't seem to use it how you do and draw conclusions as you do. If it breaks when you think about it in your interpretation then perhaps it is your interpretation that is wrong?

So, let us get back to the point in hand.

You can't define strength, or explain why size means things can't be measured because that is not the point of your system. OK.

Go away and complete (if it can be done as it might be infinte!) your school of thought. When you write something in a forum like this that is predicated on being mathematical expect people to react neagtively, because you are using non-mathematical arguments to show why maths is wrong. That is not a sensible attitude.

 

[Organic]

Dear Matt,

I answered your questions, but you want the impossible to be possible, which in this case is like:

"Please explain to me what is a color, but use only black and white".

 

[matt grime]

No, Doron, you used the phrase

'too strong to be measured'

I would like you to explain what that means.

what does strong mean in this case?
you didn't define it, just used it
what does measure mean?
you gave no explanation of measure.

what does the phrase

'top line has two results'

mean? that is a question about the meaning of the sentence in english, not maths.

 

[Organic]

Dear Matt,

Please show how you check 1-1 map between a collection of infinitely many objects and infinitely long object.

 

[matt grime]

That question would appear to require me to accept your complementary logic stuff.

Is this near?

Let S be the set of all real numbers, this is a collection of infinitely many objects.

Let T be the Real Line, this is an infinitely long object, I think.

let f be the map f(x) = x

this is clearly injective: if f(x)=f(y) then x=y

As you stated it you need to explain what the hell you mean by your terminology again.

 

[Organic]

The Full set(= {__}} is constructed by exectly 0 infinitely many objects.

Therefore |{__}| = 1.

So, show me again how can you check 1-1 map between R collection and {__}.

 

[matt grime]

Oh dear Doron, you aren't doing very well are you?

The full set, whatever you now think that might be, contains exactly one element? What a load of garbage.

In what way did my example fail to meet our criteria?

This fullset contains exactly zero infinitely many objects?

You are aware that makes no sense as a sentence. Oh sorry, it's constructed by zero exactly infinitely many objects. Well, that also makes no sense.

You define {__} to be 'the point at infinity' of the Riemann Sphere.

Why would I want to put that in bijective correspindence with R? That is not a pointful exercise. It isn't possible, but so what? That it isn't possible is no more relevant than the fact there is no abelian group isomorphic to S_5.

Your private definitions and interpretations don't interest me, what does is your attempts to construct all the strings of 0s and 1s using the axiom of infinity. Which is totally unjustified but you do it anyway.

You're confusing sets and their elements again.

But once more you refuse to explain your terminology, and side step explaining what it means for a set to be too strong to be measured... do you think you've won any disciples by omitting this?

 

[Organic]

Mr. Matt,

You write to much.

...It isn't possible...

but this is the sum of it, and you right about that.

{___} content which is ONE infinitely long object, is unreachable by any collection of infinitely many objects, and it is the top limit of Math language.

Its oppsite is the "content" of {} which is the bot. limit of Math language, and it is unreachable by any content of a non-empty set.

Shortly speaking: ({},{__}):={x|{}<--x(={.}) AND x(={._.})-->{__}}.

Please read again this including all its links:

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

Aleph0 value is under the lows of propability, because no collection of infinitely many objects can reach the contents of {} or {__}.