The 4th Dimension

If we were exclusively 3 dimensional beings, then we would not be able to experience a 3 dimensional world. Why? Below is the reason:

Construction:

  1. Circle is a geometrical construct that needs two dimensions for its construction.
  2. The construction of a circle is possible only in a 2-D space.
  3. Two dimensional space is a necessary and sufficient condition for the construction of a circle.
  4. When we say that a certain geometrical or topological construct is N dimensional we mean that an N dimensional space is the necessary and sufficient condition for its construction.

Perception:

  1. Circle as a 2-D construct can be perceived fully only from above, from above the 2-D space in which it is constructed.
  2. To fully perceive a circle one needs to transcend the circle’s space.
  3. One has to be transcendent to the circle in order to perceive the circle, or else the circle itself will be transcendent to one’s perception.
  4. Circle in its entirety is always a transcendent shape to the immanent
  5. In order to perceive a circle in its entirety, the shape of the circle, one has to step into the third dimension, a dimension that is transcendent to the dimensions of the circle and yet contains the space of the circle.
  6. The condition for a perception of the 2-D totality of a circle is being in a space that is both transcendent to the space of the circle and yet contains the space of the circle as immanent.
  7. To perceive an N dimensional shape in its entirety one has to be placed in the N+1th

Conclusion:

  1. To perceive (experience) the N dimensionality of a space, rather than deducing and inferring it, one has to be transcendent to it, being located in an N+1 dimensional space.
  2. For an N dimensional space to be perceived (experienced) it has to be immanent to the observer’s consciousness, but this immanence is possible only if the observer is transcendent to the observed, hence enjoying a higher dimension than the observed.
  3. The dimensionality of an N dimensional space is always transcendent to the observer located in the same space.
  4. The dimensionality of a space becomes immanent only and only for an observer that is transcendent to that space.
  5. Our experience of 3-D space is immanent: We intuit the 3 dimensional character of our space immediately and don’t need to deduce or infer it by examination and investigation.
  6. The 3-d character of our space is given to us immediately; it is immanent.
  7. Since our experience of the world is already 3 dimensional and immanent, therefore we have to be transcendent to it and located outside of it.

                                                                                                      QED.

 

    ***To experience two dimensionality directly one has to be in the third dimension. Therefore to experience three dimensionality one has to be in the fourth dimension.                                                    

12 thoughts on “The 4th Dimension

  1. I get the idea and understand the image. I am not a good enough mathematician to truly follow your simple math. My take: I do remember being taught that one and one makes two. But I really think that one and one makes three. Reason: there is no one. One and zero and the same. As soon as there is one, there is two because there is an inside and an outside. That makes two. I repeat, there is no one. In order for the two to conceive of an inside and an outside, there must be another dimension. Two lines cannot come together without a third line. The third line is essential for any existent closed space. The simplest form is the triangle. One line can only come together as a circle. This too encloses the space and requires an inside and an outside. You are right to show that in order to see the circle, one must transcend it. A circle within itself is not even two dimensional, but has no dimension at all. A circle within itself cannot know that it is a circle. It can only be seen from above and that adds a third dimension, so one and one still make three.

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    1. Thanks for your comment. I still didn’t get your argument of one and one making three. But a contradiction lies here: What is three? If you define three to be three ones, then one and one cannot be three. That one and one is two is already embedded in the definition of three. If one and one makes three, then three cannot be the same as three ones, or the number three for that matter. That 1+1=2 is not just a matter of fact; it is logical necessity and cannot be contradicted in principle: Here is the proof: We assume you’re right; let us say 1+1=x, and x is not 2. In fact let us assume x can be any number except 2. now from this equation 1+1=x you can subtract 1 from both sides without changing the equality: (1+1)-1=x-1. But (1+1)-1=1. Therefore, our equation reduces to 1=x-1. But this equality hold if and only if x=2. You see, assuming that 1+1 is not 2 proves that 1+1 is 2. But I am guessing you already know this and perhaps you intended to say something different, maybe imply something other than pure numbers?!
      Another ambiguity for me is what do you mean when you say circle within itself is not two dimensional?

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    1. What do you mean by projected dimension? A fourth dimension by definition lies outside, perpendicular to, the 3-D space. The best way to grasp it is to see how 2-d space compares to 3-d space. Then extend the same logic from 3-d to 4-d, though it remains impossible to visualize or imagine 4-d space but the comparison helps.

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