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What are dimensions?

  1. Apr 19, 2003 #1
    Almost everything what we are speaking about in physics, in math, in religion, ... is related to "dimensions". It's an essential concept.
    Dimensions are although used in several ways creating thus confusion.
    Do we have to create new definitions for the different use?


    Main Entry: 1di·men·sion

    Function: noun
    Etymology: Middle English, from Middle French, from Latin dimension-, dimensio, from dimetiri to measure out, from dis- + metiri to measure -- more at MEASURE
    Date: 14th century
    1 a (1) : measure in one direction; specifically : one of three coordinates determining a position in space or four coordinates determining a position in space and time (2) : one of a group of properties whose number is necessary and sufficient to determine uniquely each element of a system of usually mathematical entities (as an aggregate of points in real or abstract space) <the surface of a sphere has two dimensions>; also : a parameter or coordinate variable assigned to such a property <the three dimensions of momentum> (3) : the number of elements in a basis of a vector space b : the quality of spatial extension : MAGNITUDE, SIZE c : a lifelike or realistic quality d : the range over which or the degree to which something extends : SCOPE -- usually used in plural e : one of the elements or factors making up a complete personality or entity : ASPECT
    2 obsolete : bodily form or proportions
    3 : any of the fundamental units (as of mass, length, or time) on which a derived unit is based; also : the power of such a unit
    4 : wood or stone cut to pieces of specified size
    5 : a level of existence or consciousness

    I want to invite you to read an article of Michio Kaku: HyperSpace : A Scientific Odyssey, that you can find (in link articles) on entering the http://www.mkaku.org, : (quote)"To see how higher dimensions helps to unify the laws of nature, physicists use the mathematical device called "field theory.... In other words, by adding the fifth dimension, we have trivially unified light with gravity. In other words, light is now viewed as vibrations in the fifth dimension. In five dimensions, there is "enough room" to unify both gravity and light."

    In math's and physics "dimensions" are just added like if we were God.
    Then we try to explain interrelationships to explain concepts like the Calabi-Yau spaces.
    But isn't this LAYERING?

    Dimensions represent also our daily physical world (related to "perspective"). But there are a lot of questions, such as: are dimensions 'isolated'. Isolation seems logic since we are unable to observe higher dimensions.

    But also does it make sense to call TIME a dimension? Isn't it adding apples to oranges? Isn't time a quality (progress) of the physical processes? Can't we explain space-time in another way?

    Are we trapped in word games? Do we have to rephrase?
  2. jcsd
  3. Apr 19, 2003 #2
    What are dimensions? Boundaries, or limitations of that which is held "in context."
  4. Apr 19, 2003 #3
    Boundaries = thus isolated?
    Limitations = thus till there is a point, a field, a line which blocks. Thus valid in a certain area = isolated field.

    Isolation is in my opinion one of the essential concepts in cosmos next to interaction and movement.

    Now: are dimensions inter-involved, intertwined, inter-crossing... or interacting?

    Here we see already that the actual definitions are contradicting depending from math and the physical world. In math you can exclude but can you in (what we call) the physical world?
  5. Apr 19, 2003 #4
    So we should accept everything as a whole first, before we begin to make distinctions ... Right?

    I think little children are very good at that, but little children are also naive. Now, if only we could remain as little children and still be able to differentiate? ...
  6. Apr 19, 2003 #5
    The Mystery Within

    From the thread, The Mystery Within

  7. Apr 19, 2003 #6
    Fractal geometry speaks to the need to redefine dimension just as QM speaks to the need to redefine logic. In both cases what has become evident is that broader definitions are more useful for specific purposes if not so useful in everyday life. As has historically been the case more often than not, when our abstractions become more convoluted we don't throw out the old and replace it with the new. Instead, we build the new upon the old and retain the use of both.

    Essentially, there are two ways of going about this process of redefining dimension. We can attempt to modify the existing definitions, thus taking the semantic and logical route, or we work backwards from the physical evidence. Both of these routes have so far focused on contextual definitions which is exactly what your dictionary definition points out as well.

    Notably, there are two basic contexts in the dictionary definition of the word: the personal and physical. As with QM, blurring the lines between these two contexts will provide a yet again more useful definition of the word. In fact, the word context itself is a merely another aspect of dimension and, thus, the dictionary definition is self-referential, self-contradictory, and Indeterminate.
  8. Apr 19, 2003 #7
    The Kaku link doesn't work, did anyone else notice that?
  9. Apr 19, 2003 #8
  10. Apr 19, 2003 #9
    Thanks, will take a look in Fractal geometry.

    Since I like to 'see' the mechanics the second way is more appealing.
    All depends what we call physical evidence, since so much is perception (just look to all subjects in these forums).

    For some of us (me included) reality is not just something you can put into a box, there is more. So the proof of evidence is on our side.
    For others reality it just weight, length, numbers, ... .

    Persons are of course part of the Physical.

    A abstract formulation could be: "A Dimension is an area in overall balance in which at least one internal parameter has the ability to act."
    Area: aspect of unity (isolated from other dimensions) within limits /boundary, relative self-sustaining.
    In overall balance = interior unbalance stays possible.
    Internal parameter can be: a value, a person, conscious, a sub-dimension, a point, ...
    Ability to act: parameter can stay inherent, move, interact, travel, ... .

    Just a try ...
    Last edited: Apr 19, 2003
  11. Apr 19, 2003 #10


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    Mathematical concepts, what else ? :wink:
  12. Apr 19, 2003 #11
    This is being contested today by neurologists and radical behaviorists in particular. Emotions and affect are critical to both the formation of logic and perception and provide a clear way to bridge the mind body dichotomy of traditional western sciences and philosophy. However, I believe you are correct that a great deal of work needs to be done in this area before it can scientifically applied to such abstract concepts as "dimensions".

    This is precisely why a good definition of dimension must contain the personal as well as the geometric.

    As well as the mental. No mind, no person.

    This is a pantheistic interpretation of dimension. A more mystical one would be paradoxical, indeterminate, etc. For a Panentheistic theory such as your own both are required. Therefore you could modify this definition considerably.

    Exactly what a dimension is remains ambiguous, but useful mechanical tautological definitions can be created using examples in nature such as Relativity and Fractal geometry supply. Such are already being attempted, but other than that I don't know any details on the subject. A fractal discription of QM is also being attempted, but the math is horredously difficult even by the standards of String theory.

    Essentially, Fractal Geometry asserts there is such a thing as a "fractional dimension" and how this might modify the axioms of geometry is the thing no one has figured out yet. Like a lot of holistic theories, the devil is in the details.
  13. Apr 19, 2003 #12
    Dimensions define the form, by which the essence is contained within.
  14. Apr 19, 2003 #13
    Thx Wu Li,

    you are indeed a lateral thinker. ;-)
    You know what I am going for.
    You know. You remember.
    My Tao is not intentional pantheistic but leads to there for those who want to find that.
    My theory doesn't need dimensions. You know too.

    But I want to analyze dimensions since it seems to be trap for a lot of people and to be intellectual satisfactory for others.

    For those interested:

    Fractal Geometry: A Simple Explanation
    Where classical geometry deals with objects of integer dimensions, fractal geometry describes non-integer dimensions. Zero dimensional points, one dimensional lines and curves, two dimensional plane figures like squares and circles, and three dimensional solids such as cubes and spheres make up the world as we have previously understood it.

    However, many natural phenomena are better described with a dimension part way between two whole numbers. So while a straight line has a dimension of one, a fractal curve will have a dimension between one and two depending on how much space it takes up as it twists and curves (Peterson, 1984). The more that flat fractal fills a plane, the closer it approaches two dimensions. Likewise, a "hilly fractal scene" will reach a dimension somewhere between two and three. So a fractal landscape made up of a large hill covered with tiny bumps would be close to the second dimension, while a rough surface composed of many medium-sized hills would be close to the third dimension (Peterson, 1984). http://archive.ncsa.uiuc.edu/Edu/Fractal/Fgeom.html

    But: Fractal geometry can not offer me the complexity and levels of freedom that are reached with only a few pelastrations.

    In the pelastration concept a dimension is simply a layer with specific properties and position depending from the joined tubes. In this dimension all kinds of sub-dimensions may occur.
  15. Apr 20, 2003 #14
    Interesting articles on time , including: Is time the fourth dimension?

    (follow link supplement)


    Is time the fourth dimension?
    "Yes and no; it depends on what you are talking about. Time is the fourth dimension of spacetime, but time is not the fourth dimension of space, the space of places.

    Mathematicians have a broader notion of the term 'space' than the average person; and in their sense a space need not consist of places, that is, geographical locations. Not paying attention to the two meanings of the term 'space' is the source of all the confusion about whether time is the fourth dimension. The mathematical space used by mathematical physicists to represent physical spacetime is four dimensional and in that space, the space of places is a 3-d sub-space and time is another 1-d sub-space. Minkowski was the first person to construct such a mathematical space, and he was the first person to call time the fourth dimension, because it was the fourth dimension of his abstract space for spacetime. But spacetime is represented mathematically as a space of events, not a space of ordinary geographical places such as the place where the sun is located and the place where London is located.

    In any coordinate system on spacetime, it takes at least four independent numbers to determine a spacetime location. In any coordinate system on the space of places, it takes at least three. That's why spacetime is four dimensional but the space of places is three dimensional. Actually this 19th century definition of dimensionality, which is due to Bernhard Riemann, is not quite adequate because mathematicians have subsequently discovered how to assign each point on the plane to a point on the line without any two points on the plane being assigned to the same point on the line. The idea comes from Georg Cantor. Because of this one-to-one correspondence, the line and the plane have the same number of points. If so, then the line and plane must have the same dimensions according to the previous definition. To avoid this problem, the notion of dimensionality of a space has been given a new, but rather complex, definition."
  16. Apr 20, 2003 #15
    As absurd as it may be in some respects, your theory is a physical theory and, thus, it must be framed within a Pantheistic, Panentheistic, or other paradyme compatable with science. For that purpose mysticism just won't do. :0)
  17. Apr 20, 2003 #16
    The Fourth Dimension?

    If you have a three dimensional form that exists within space, as well as the space that the exists within the form, what does that make space, the fourth dimension? Or volume? (i.e., within the entirety of space itself as well as within the form). And why is the Greek letter dela, essentially an equilateral triangle, called "the fourth?" Is it referring to the space, or fourth dimension, inside the triangle?

    The reason why I say this is because it takes the first three dimensions to define to the fourth, and hence the "volume within" (as well as without, which exists within the entirety of space itself).
  18. Apr 20, 2003 #17


    I am in QM now, solving your paradoxes.

    Essential to Q Leap is that on arrival of the system S (two pelastrated tubes = entangled = acting as wave) in resonance field of M (measuring divice) the M provokes de-pelastration (redraw by polarity or disharmony) of the transport tube and (free-ed) particle tube (still composed tube) becomes visible after new pelastration with M (absorbed = measured, but absorbed doesn't mean united, just joined). In P every quanta is the result of previous pelastrations each tube keeping it's properties till de-pelastrated to more basic components.

    I think P-approach is a structural(?) theory, not a physical.
    (do you know I invented already some new toys based on Pelastration, under patent already, and already prototypes ;-)). Can become the new POGS ... who want to invest?)

    Making designs now for web.

    This (draft) has potential. Just need to formulate it more detailed. But the P-mechanism can handle it.

    Some related stuff (from http://plato.stanford.edu/entries/qt-measurement/):
    Qoute: "The post measurement entangled state of S+M, SUM cifi (X)gi, is a "pure state", represented by a single Hilbert space vector. There are, however, other sorts of states in QM, namely "mixed states", represented not by single vectors but rather by so called density operators. It is characteristic of S being in a mixed state that, from the point of view of statistical distributions over possible results of measurements on S, S behaves as if, for some set of vectors {fi} and some set of numbers {pi} for which SUM pi = 1, there is probability pi that S is in the state fi, for i = 1,2,.... (Mathematically, such a state is represented by a so-called density operator, SUM pi |_fi><fi_|, where |_fi><fi_| is the projection operator onto the vector fi.[14]) Von Neumann proved that when S+M is in the entangled state SUM cifi (X)gi then S is in such a mixed state. In particular, S behaves as if there were probability |ci|2 of being in state fi, for i = 1,2...; similarly M is in a mixed state, behaving as if there were probability |ci|2 of being in state gi, for i = 1,2....(von Neumann 1955, 424)."
  19. Apr 20, 2003 #18
    Re: The Fourth Dimension?

    Interesting questions, making me to ask: are dimensions relative to the observer.
    In the previous article it is clear that time as D4 is intended and related to spacetime and not to our living space. (Quote: " ...But spacetime is represented mathematically as a space of events, not a space of ordinary geographical places such as the place where the sun is located and the place where London is located.")

    Look to your own body. Our body has coordinates in our 3D world. We have our 24h time-appreciation. But inside our body you have a transport , electrical and energy system, etc with internal coordinates which have no real relationship with our "standard" 3D world. We even have only a partly idea how it works. There is a varity of completely different type of interactions and other time-frames. On the lowest level we find DNA storeing our essence. But they again are composed from lower building boxes till we sit on the particle level.

    These level of existence are all related with each other but we can say that they have another dimensional relevance. On the level you are resonant with you have access. So our 3D world is as a whole a layered system where Delta's have Delta's have Delta's ... inside. = infolded.
  20. Apr 20, 2003 #19
    Re: Re: The Fourth Dimension?

    But space exists both within and without and the only thing that seperates it is "three dimensional" form. Therefore, what dimension is space?
  21. Apr 20, 2003 #20
    Re: Re: Re: The Fourth Dimension?

    Maybe you have to reverse your statement to: ... and the only thing that JOINS us is "three dimensional" form.
    It might make sense to see your body as a small universe (a separte universum with its own dimensional realities) inside a much larger universe (that we call earth and space).
    Delta in Delta, ...

    A condition to such approach is that our super-dimension must be isolated (to keep it's structure, internal interaction, specificities and internal dimensioning) versus the surrounding dimensions, but also must have the tools to interact (to get energy, air, etc ). Another aspect will be the consciousness. Awareness can be seen as a synergic energetic level (cooperation) between several acting layers resulting in the ability of observation. Thus observation of the surrounding as being DIFFERENT from the own unity (ME : being the collectivity of various interconnected dimensions). As observer you will have the possibility to act independent from the surrounding world and make choices. Even in conscuiosness there will be different levels such as intellectual operations, emotions, ... .

    This make me say that the basic mechanisms in the universe are movement, isolation and interaction. These fundamental processes must be jointed.
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