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Organic Mathematics

  1. May 16, 2004 #1


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    Most books that teach the language of Mathematics, ignore our cognition’s abilities to understand and define the fundamental concepts of this language.

    Language is a tool that gives the cognition its ability to examine the object, the subject and the value of object/subject relations.

    For billions of years, living things have been learning how to deal with internal and external challenges occurring in their ways, and as the phenomena of life becomes more and more complex, it needs better tools of communication that will give it the ability to save and develop life from the single gene to the existence of civilizations.

    The language in its both inherited and purchased sides is the most significant environment of life phenomena, and through it life can flourish from generation to generation.

    Any language is examined first of all by its ability to express at least two opposite properties: the simple and the complex.

    This basic polarization is the clearest signature of reality in the global memory of life, and this memory is the guarantee to their existence.

    Because of this insight, we as living things have to take extra care when we are using a powerful language like Mathematics, because it has the straightest influence on our own survival.

    An imprecise use of this powerful language (when the meaning of “precise” is not just technical formal precision but the ways of using its products to support and develop life) can quickly bring us to a dead-end.

    Our abilities to avoid it are connected with our abilities to understand the deep relations between language, reality and the cognition that involved with them.

    Through this participation, we can tune our life and lead them away from a dead-end.

    The first hints to an imprecise use of this powerful language can be found when we are loosing our abilities to distinguish between the simple and the trivial and between the complex and the complicated.

    The opposite of the trivial is the complicated, when by saying “trivial” we mean a non-deep reference between the cognition and the thing(s) it is referred to.

    For example: our belief that our models are equivalent to reality, which leads us to the trivial conclusion that what holds in our models also holds in reality.

    The indistinguishability between the complex and the complicated appears when the cognition tries to force its trivial conclusions on the reality, but then it become aware to the complexity of the reality and concluding that reality is complicated.

    A question that should be asked by any civilization that is using a powerful language like Mathematics is: can we find signs of using Math in an incorrect way?

    I think that a very brief look on our civilization gives us too many signs of complicated paths that lead us to nowhere.

    If we want to avoid these obstacles, I think we have to include methods which reflecting the influence of a powerful language like Mathematics language on our life.

    By this approach we get at least two main advantages:

    a) Quality control based on tuned dynamic balance of the influence of Math language on our cognition, which supports our cognition's abilities to deal with abstract and non-abstract non-trivial complexity of the real life.

    b) An improved ability to create deep and versatile relations between opposites, which give us better and more valuable conditions for flourishing life.

    So the first step to this goal is to reexamine fundamental concepts through this approach.

    Let us start by checking our ability to count.

    The eye does not see itself until it is aware to its own limitations, and then it can be included as an explored element.

    Now please change "eye" by "cognition" and read the above again.

    The above point of view leaded me to ask myself what are the minimal conditions that give us the ability to identify and count things?

    For example, let's examine this situation:

    On the table there is a finite unknown quantity of identical beads > 1
    and we have:

    A) To find their sum.

    B) To be able to identify each bead.

    Limitation: we are not allowed to use our memory after we count a bead.

    By trying to find the total quantity of the beads (representing the discreteness concept) without using our memory (representing the continuum concept) we find ourselves stuck in 1, so we need an association between continuum and discreteness if we want to be able to find the bead's sum.

    Let's cancel our limitation, so now we know how many beads we have, for example, value 3.

    Now we try to identify each bead, but they are identical, so we will identify each of them by its place on the table.

    But this is an unstable solution, because if someone takes the beads, put them between his hands, shakes them and put them back on the table, we have lost track of the beads identity.

    Each identical bead can be the bead that was identified by us before it was mixed with the other beads.

    We shall represent this situation by:

    ((a XOR b XOR c),(a XOR b XOR c),(a XOR b XOR c))

    By notating a bead as 'c' we get:

    ((a XOR b),(a XOR b),c)

    and by notating a bead as 'b' we get:


    We satisfy condition B but through this process we define a universe, which exists between continuum and discreteness concepts, and can be systematically explored and be used to make Math.

    It means that what is called Natural number is at least a structural/quantitative information form.

    Standard Math axioms that define the Natural numbers ignore our cognition's abilities to define them, and the result is a quantitative-only information form where cardinality (quantity) and ordinality (order) are both well-defined.

    By this attitude, Standard Math is not aware of several structural/quantitative information forms that exist within any given quantity > 1, and uses only the wall-defined information forms that have no redundancy and no uncertainty.

    By using Organic Mathematics ( http://us.share.geocities.com/complementarytheory/OrganicMathematics.pdf ), any number is first of all an information form that can be understood only by cognition/object interactions.

    From this point of view, redundancy and uncertainty cannot be ignored and they are taken as "first-order" (fundamental) properties of Math language, which is a paradigm shift of the Natural numbers concept that open for us a gateway to complexity.

    Last edited: May 22, 2004
  2. jcsd
  3. May 16, 2004 #2

    matt grime

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    so the basic objects of our theory aren't basic but more complex, how uninteresting.
  4. May 17, 2004 #3
    seems extremly tedious.

    he does say .999~ ≠1 which i like, but he doesn't really explain why other than "he has defined it to be so"

    my way is better ;D
  5. May 17, 2004 #4
    Does a dodgy kebab still contain the golden ratio?

  6. May 17, 2004 #5


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    No dear,

    They are private cases of a much more interesting universe.

    Your excluded-middle reasoning cannot deal with complexity because it is based on an information form where redundancy_AND_uncertainty are not "first-order" properties.

    In this case you have no tools to explore and understand redundancy_AND_uncertainty because your excluded-middle first-order tools are nothing but a one tiny private case of some well-defined information forms that have no ability to deal with information forms, which redundancy_AND_uncertainty are "first-order" properties of them.

    Has I keep saying Matt, you prefer to deal with a language which is very good when you research the ballistic path of a one dead bird throwing in the air.

    What I suggesting is a theoretical system that can deal with a folk of flying living birds (whrere your research of the ballistic path of a one dead bird throwing in the air, is a trivial case of it).
    Last edited: May 17, 2004
  7. May 17, 2004 #6


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  8. May 17, 2004 #7


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  9. May 17, 2004 #8
    that may work when you're starting with an "object" on which two "points" are defined and they're both moving towards the limit at the same rate

    but with numbers we're defining a single point to begin with such that it cannot get "smaller"

    i'm interested to see how organics can define such a convergence using a single point moving in 1/2 distances to a destination.

    PS] shouldn't it be "the more distance you cover, the smaller you become" not "the faster you drive"?
  10. May 17, 2004 #9


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    There is no such an objective thing like a "number" but only an information form that depends on the way we defines it.

    Even though every notation's place that existing along some infinitely long fraction, defining values that becoming smaller but always they are bigger than zero.

    What you call a point is no more than a break point which is the result of your measurement and it does not exist before you measure it.

    Our place value representation system has a structure of a fractal, which its main property is a self similarity upon different scales, where the depth of this fractal can be finite or infinite.

    When this fractal has an infinite depth, then our shrinking sport car cannot complete its mission.

    In the same manner the invariant symmetry of e>d>0 always exist, unless we break it by an arbitrary phase transition between some scale to zero, and vise versa.
    Well, let us look on this situation as SR Lorenz-like transformation.
    Last edited: May 17, 2004
  11. May 17, 2004 #10
    so if i'm grasping this correctly it's two dimensional math insofar as the way numbers and values are held instead of linear one-dimensional math that we currently use. (if so then those pictures start to make some sense ;D )

    i could see the potential power in computing with such a system just as quantum computers that could calculate with 3 states would be far superior to the digital binary computers using 2 states that we use today.
  12. May 18, 2004 #11


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    Dear ram2048,
    You are starting to get the picture, my quantitative/structural information forms are multi-dimensional parallel/serial building-blocks of a non-trivial number system.
    Because my system is based multi-dimensional parallel/serial building-blocks, where reduncancy_AND_uncertainty are taken as first-order properties, I think we have in our hands a better tool to deal with complexity, including computation problems.
  13. May 19, 2004 #12


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    But in my opinion the important point is that no real change in any scientific field (abstract or non-abstract) will take place, if we ignore our own cognition's abilities to develop these areas.

    The power of any scientific method has to be balanced by a language that give us the ability to distinguish between the simple and the trivial from one hand, and between the complex and the complicated from the other hand.
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