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The power of the transfinite system

  1. Jan 13, 2004 #1
    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
     
    Last edited: Jan 13, 2004
  2. jcsd
  3. Jan 13, 2004 #2

    Hurkyl

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    But {__} has been reached by your system, thus your system cannot have any information in it! (Otherwise it would be an information system, right?) :smile:
     
  4. Jan 13, 2004 #3
    Last edited: Jan 13, 2004
  5. Jan 13, 2004 #4
    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.
     
  6. Jan 13, 2004 #5
    Dear master_coda,

    You wrote:
    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
     
    Last edited: Jan 13, 2004
  7. Jan 13, 2004 #6
    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.
     
  8. Jan 13, 2004 #7

    matt grime

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    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
     
  9. Jan 13, 2004 #8
    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
     
    Last edited: Jan 13, 2004
  10. Jan 13, 2004 #9
    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.
     
  11. Jan 13, 2004 #10
    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".
     
  12. Jan 13, 2004 #11
    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.
     
  13. Jan 13, 2004 #12
    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.
     
  14. Jan 13, 2004 #13
    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.
     
    Last edited: Jan 13, 2004
  15. Jan 13, 2004 #14
    Whats the point of calling it aleph0 if you don't have aleph1, aleph2, etc. ?

    Any concept in any model can be changed.
     
  16. Jan 13, 2004 #15
    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 {__}.
     
  17. Jan 13, 2004 #16
    Call it {___}. At least that'll help avoid equivocation.
     
  18. Jan 14, 2004 #17
    Thank you Master_coda, I'll call it Full set (which is the opposite of Empty set).
     
  19. Jan 14, 2004 #18

    matt grime

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    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?
     
  20. Jan 14, 2004 #19
    Last edited: Jan 14, 2004
  21. Jan 14, 2004 #20

    matt grime

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    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.
     
  22. Jan 14, 2004 #21
    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
     
    Last edited: Jan 14, 2004
  23. Jan 14, 2004 #22

    matt grime

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    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.

    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.
     
  24. Jan 14, 2004 #23
    If you don't read my major theorem about math by principle then this is my last reply to you.
     
  25. Jan 14, 2004 #24

    matt grime

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    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.
     
  26. Jan 14, 2004 #25
    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
     
    Last edited: Jan 15, 2004
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