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Thread: Theory that reduces complexity of dimensions to base units

  1. #1 Theory that reduces complexity of dimensions to base units 
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    I apologize in advance for doing this in 3 parts...

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    PART 1
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    Abstract

    This theory reduces the dimensions down to a base algorithm that provides the "rules" for defining dimensions. It can be used to: predict the structure of any/all dimensions; and to help visualize how what we observe about our space and universe may be explained by that definition.

    Defining the 4th Dimension and Beyond

    Hypothesis and Basis for My Model


    Standard Geometry tells us about the properties/rules of points, lines planes and spaces…

    • A point has no form, as it is infinitely small.
    • A line has only length, is comprised of at least 2 points, and is infinitely long.
    • A plane has two dimensions (length and width, x,y only), a flat surface area with no thickness that extends infinitely, and its area is comprised of points and lines.
    • A space has three dimensions—length, width, and height (x,y,z), and its area is comprised of points, lines, and planes.

    We also know that…

    • A minimum of 2 points are needed for a line to exist.
    • A minimum of 2 lines (parallel or intersecting), or 1 line+1 point, are needed for a plane to exist.
    • A minimum of 2 planes (intersecting or parallel) are needed for a space to exist.

    So, if we had a minimum of 2 spaces, what would now exist? (And following that logic, I wondered what a “parallel” or “intersecting” space would look like.)

    Since the dimensions already were defined by numbers (and to make it easier on myself so I wouldn’t have to re-program my brain when thinking this through), I used the existing numbers. However, a point didn’t have any number, but since it was infinitesimally small, and since a zero would work for the sequence, I assigned the “dimension” 0 to a point. (I did feel good when I later found out that the science field had also decided to adopt that convention. And, it makes this part of the explanation easier.)

    Using the dimensional numbers to represent the elements that define each dimension, we have…

    Dimension Defined by
    0 ------- Point
    1 ------- Line
    2 ------- Plane
    3 ------- Space
    4 ------- ???

    Trying to visualize going from one space to another...in order to do that, you would have to go through *something.* Time? Space-time?

    To help visualize that part, I went back and thought about pretending I was that two-dimensional (flat) being, living on a single plane. That plane would, then, be my entire universe—any other plane would be a different universe. In order to get from one plane to another, the “something” that I would have to traverse would be a space. That is because, to get off that plane, the only direction I could go is “up” or “down”—aka 3-D. Trouble is, I would not have any knowledge about “up” or “down” because my perspective is limited within my plane-world. Likewise, in my 3-D world, it’s hard to imagine a fourth dimensional direction I would need to traverse to get to to a "different" space.

    In considering how we would get between any of the other dimensions…

    Going between two Points — you would have to travel along a Line.
    Going between parallel Lines — you would have to travel on a Plane.
    Going between parallel Planes — you would have to travel through Space.
    Going between [parallel?] Spaces — you would have to travel across ????

    Given that, a space could also be defined as a whole bunch of planes stacked on top of one-another. So, what is it I would need to traverse to go between spaces? It would be something that contained a bunch of spaces? That *something* would, of course, be the 4th dimension. Like the planes all stacked up to create a space…what if we were to stack a whole bunch of spaces—what would it create? What would it look like?


    Last edited by the alien blogger; February 19th, 2013 at 02:48 PM.
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    ----------------------
    PART 2
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    The Minimal/Triangular Space Model

    I thought it might be easier if I could pare down space to a minimal size. If I could better define what a “space” actually is. So, what is a space?

    Space is a three-dimensional area. How do you define three dimensions? One way, of course, is with x, y, and z coordinates But I needed something much more basic—something that would be the minimal, base structure of space, and preferably of each dimension.

    I thought about the least number of elements needed to create each dimension. What would be the least possible number of points to define each dimensional object…

    LEAST POSSIBLE POINTS

    Points=Dimension
    1 = Point = 0
    2 = Line = 1
    3 = Plane = 2
    4 = Space = 3
    5 = ???? = 4

    We can then interpolate that the fourth dimension would be defined with a minimum of 5 points.

    Now, we only have to figure out where that fifth point needed to go. Where would it go? What would a least number of points *look* like?

    VISUALIZATION
    o = 1 Point = Dim 0
    o----o = 2 Points = Dim 1
    ....o
    .../ \
    o --- o = 3 Points = Dim 2

    [tetrahedron] = 4 Points = Dim 3

    ??? = 5 Points = Dim 4

    The least possible points reduces it to TRIANGLES. And the least elements, then, would logically be an equilateral triangle. If everything was equal, the 4th dimension would also require the spacing of the points to be equal, the length of the lines to be equal, the size of the planes to be equal, etc.

    The only place that was *equally* too short for all points and planes was the dead-center. If that center somehow burrowed in deeper than just our space—poking through to a "fourth dimension."

    Expanding on that, we would have...

    D...o..L..P...S..4d
    --- -- --- -- --- ---
    0> 1- 0- 0- 0- 0
    1> 2- 1- 0- 0- 0
    2> 3- 3- 1- 0- 0
    3> 4- 6- 4- 1- 0
    4> 5-10-10-?- ?

    Where D=Dimension, o=Points, L=Lines, P=Planes, S=Spaces, 4d=4th D

    One can interpolate that the number of spaces for the next dimension would be “5.” There are, of course, other numbers that could be easily inferred. And, this could be used to postulate “negative” dimensions (could those apply on a sub-atomic scale?)

    Looking at the pattern, it is clearly a section of Pascal's Triangle. That is potentially significant, and it makes sense.


    Last edited by the alien blogger; February 19th, 2013 at 02:47 PM.
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    ---------------------------
    PART 3 - Final part
    ---------------------------


    White Holes—Tying It All Together With Some Tantalizing Theories

    What would the actually look like? If the extended space bulges so far inside, that it pushes out into another 'place,' it would be a sort of an “anti-space” projection on the other side of that pinhole. This becomes a tesseract--but a triangular version--that hasn't yet been represented. (The image looks a bit like a crystalline structure).

    Apparently, it involves 'poking a hole' through our existing universe. Black holes, crush everything down to a very small point—crushing so hard, they could be poking a hole right through to another “space” in another universe-- which would mean that both spaces together would comprise a fourth dimensional existence.

    Is time the fourth dimension? It's more likely a time-space, as the “event horizon” would imply that. It could also be something more exotic.

    There are several questions this suggests...

    * Are photons a real-world example of dimension 0?

    * What if our “big bang” in this space/universe of ours, is actually a black hole that imploded in another universe and is now leaking in from another space/universe—a WHITE hole here?!

    * What if all of the black holes we see here have little spaces poking out into other universes—becoming ‘white holes’ and spawning new spaces (a bubble universe elsewhere)?

    * And could there be any other spaces 'intruding' on the edge of our space?
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    Genius Duck Moderator Dywyddyr's Avatar
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    Apart from Four-dimensional space - Wikipedia, the free encyclopedia
    I have a some quibbles:
    1) You can't define THE 4th dimension 1 - to be precise you're talking here about a/ the 4th spacial dimension.
    2) A line doesn't have to be infinitely long, nor does a plane have to be infinite in extent.
    3) "“negative” dimensions (could those apply on a sub-atomic scale?)". Huh? Why should "negative dimensions be particularly small? (See previous point. for example).



    1 THE 4th dimension depends entirely on which particular set of parameters you're considering at the time.
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    Brassica oleracea Strange's Avatar
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    I think you have developed some interesting intuitive views of plain old plane geometry (Euclidean geometry). You will probably find it rewarding to study the math behind these ideas, now you have worked this much out for yourself. And then the fact that geometry doesn't have to be based on "straight" lines and "flat" planes ... the exciting world of non-Euclidean geometry.

    Then you make a leap to black holes and even white holes. However, these cannot be described in the sort of geometry you have come up with. You need to go even further to differential geometry to be able to predict/explain/describe such things.

    An interesting idea but I think you need to learn a lot more before going any further.
    ei incumbit probatio qui dicit, non qui negat
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