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Dimensional Views [ 01.11 ] Appearance and Reality

Published: 03.03.2006
Updated: 02.07.2015
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Perhaps you may ask yourself what this mathematical/geometrical stuff is all about.
It is just to create a common base of understanding holistic structures of human consciousness, comprising keys to spirituality. Our aim is to put us in the position of someone, being in the situations described below, to find out the difference between appearance and reality from different points of view. (See: Anekant)

This is the next conceptual exercise to become aware of what we are normally not aware of - our limitations.
When we definitely recognize the limitations of each basic condition, the dimensional determinations deliver operational criterions to lead us through different appearances.

Holistic View:

  • We should rembember that higher dimensions indeed always include all the lower dimensions.
    These lower dimensions are always present and play their role.
    They exist not separated from, but are part (elements) of the higher dimension.


Point [0D]

Dimension Roles of Points
0 Point of location
1 Limiting a section of a line from point A to point B
2 Vertices of a square
3 Vertices of a cube
4 Vertices of a hypercube

  • From the 0-Dimension point of view all higher dimensions are potentially inhibited in zero.
  • All existence starts from a point.
    • To come to the point, all dimensional structures can be developed from a point.

Each dimensional condition defines the appearance of objects, according to the point of view (position) and it's direction.(line of sight)

A square [2D] can be defined

  1. as surrounded by lines [1D]
  2. as part (plane) of a cube [3D]

A visitor from a higher dimension enters and contacts a lower dimension

Dimensions on this tour: 4-3-2-1-0

Code of conduct:

As the higher dimension always contains the lower dimension, the lower dimension can recognize its own quality/form in the higher dimension. (see: Political Department of Dimensional Tour)

To be recognized/realized from/in the lower dimension, the visitor must approach in "the right way"

  1. perpendicular approach to destination
  2. remaining motionless during visit

In the following, the "visitor from" is called:

Dimension # Name
HyperSpace 4 Hyperspacelander
Spaceland 3 Spacelander
Flatland 2 Flatlander
Lineland 1 Linelander
Pointland 0 Pointlander

HyperSpacelander [4D] goes Spaceland [3D]

Some nice views [3D] on hypercubes from Hyperspace [4D] with a "star design" appearance.

To locate the hypercube visitor from hyperspace [4D] in our [3D] world, the visitor has to aproach our coordinate system with one of it's 8 cubes (parallel to x, y, z).

Arrived at the right position:

The innerst cube [3D] of the tesseract [4D] is in touch with our coordinates x,y,z [3D]

We can recognize this (coloured) cube inside our world [3D].
We are used to cubes and can learn to see them spacial.
The natural condition of Spaceland is to see objects as plane projections [2D]

The other 7 of the 8 cubes of the Hyperspacelander [4D]
remain invisible to us.

Contact: Space by space


Visitor's [4D] view inside Spaceland [3D]:

  • all bodies transparent
  • inside of bodies accessible.

Spacelander [3D] goes Flatland [2D]

3D observers's view:

A cube from Spaceland [3D] approaches Flatland [2D]

4D observers's view:

The cube is transparent

The yellow flat is the groundflat

3D observers's view:

The Spacelander's groundflat approaches parallel to the surface of Flatland [2D]

3D observers's view:

contact: Flat by flat

The cube is not visible for a Flatlander [2D]

Flatlander's [2D] view (from a distance):

A line.

Flatlander [2D] goes Lineland [1D]

3D observers's view:
A square from Flatland [2D] approaches Lineland [1D]
3D observers's view:
2D Square turns one of his sidelines parallel to Lineland [1D], to get attached to it.
Carefully watching that no inhabitant of Lineland [1D] get's moved out of existence (pushed from the line into a parallel universe), the one side of the square can become "one" with Lineland [1D].
  • Contact: Line by line.
2D observers's view (from a distance):
Lineland [1D] (blue line) entered by by a Flatlander [2D] (yellow line)
2D visitor's view into Lineland [1D]: A point [0D]
1D Linelander's view of the Flatlander [2Dvisitor]: A point [0D]

more about 1D Linelanders:

1D Linelanders differ from each other by length.
They are all sections living on the endless 1D line.
They have only 1 degree of freedom and can move only forth and back.
So everything appearing in their world looks like a point.
They are used to it.
They are normaly not aware of their 1 dimensional limitations.

Linelander [1D] goes Pointland [0D]

(This is a breathtaking intension as a Pointland [0D] has no size, only location.)

3D observers's view:
A Linelander [1D] (green line) approaches Pointland [0D]
(symbolized by a black point)
3D and 2D
Linelander [1D] correctly docking on Pointland [0D] by facing it.
  • Contact: Point to point

Pointlander's view [0D] of a Linelander [1D]: A point [0D]
? 1D observers's view:
As 0 Dimensions have only position but no size, a view is potentially possible, but there is nothing to see for the eyes.
Maybe a microscope can help....


One important feature of a higher dimension is:

From a higher dimension it can be looked "inside" the next lower dimension

  • From [4D] it can be looked inside a [3D] object (omniscience from view of [3D]) and take action (omnipotence from view of [3D]).
  • From [3D] it can be looked inside a [2D] object (omniscience from view of [2D]) and take action (omnipotence from view of [2D]).
  • From [2D] it can be looked inside a [1D] object (omniscience from view of [1D]) and take action (omnipotence from view of [1D]).
    • Any point on the line can be seen as the "inside of a line".
      A Linelander [1D] moves like a train in Lineland [1D] along the rails.
      A Flatlander [2D] can enter the line at any point from the side.
  • From [1D] it can/cannot be looked inside a [0D] object.
  • potentially it is possible
  • factual there is nothing to see.
    Aproaching 0D is possible, but reaching, touching it, is not possible, because there is no quality for our senses to dock on.
    The information about the location, the coordinates, is available.

The material world seems to end here, doesn't it.


© Christian & Carla Geerdes, Editors HereNow4U online magazine


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      1. Anekant
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      7. Tesseract
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