Tertium Organum, Chapter 3 (Space)

pillars

Reference: Tertium Organum, Chapter 2

The following is a summary as well as a commentary on Chapter 3 of Tertium Organum by P D Ouspensky:

Looking at the pattern among the first three dimensions, a higher dimension manifests new properties that are inconceivable in the absence of that dimension. So in our 3D space it is impossible to imagine the body having more than three dimensions, and impossible to understand the laws of the existence of such a body.

Therefore, Ouspensky starts out his investigation by considering what cannot be in four-dimensional space. He hopes that this will permit him to set forth what can be there.

By analogy, a “four-dimensional body” could be a tracing of the movement of a three-dimensional body in a direction that cannot be projected from the other three dimensions.

For example, time is a direction that cannot be projected from the three spatial dimensions. It is independent of those three spatial dimensions. Therefore, the tracing of the movement of a three-dimensional body in time shall produce a “history,” which may be called a “four-dimensional body.”

NOTE: The fourth dimension of ‘higher space’ does not have to be a geometrical dimension.

Again, by analogy, we may regard a 4D body as an infinite number of 3D bodies. A body with all its “history” shall satisfy that requirement. It would be limited, or outlined, by 3D bodies. Or, it would form the distance between two 3D bodies. Or, it would separate several 3D bodies one from another.

A 4D body, such as, a “historical body,” would bind several 3D bodies into a certain whole. The 4D space shall contain distances between a group of 3D solids.

By analogy, it is possible to regard the 3D solid as a section of a 4D body, and our entire 3D space as a section of a 4D space.

Ouspensky says,

If every three-dimensional body is the section of a four-dimensional one, then every point of a three-dimensional body is the section of a four-dimensional line. It is possible to regard an “atom” of a physical body, not as something material, but as an intersection of a four-dimensional line by the plane of our consciousness.

In other words, the “plane of our consciousness” is three-dimensional. That would be a moment in time.

It is possible then, that a number of 3D bodies that appear to be separate, are parts of the same 4D body. In our example, the 3D bodies that appear to be separate in a moment in time, may not be separate and be part of the same 4D “historical body,” such as, a family tree.

Just like it is possible to represent a 3D body upon a plane, It may be possible to represent a 4D body in 3D space. I think this is done in a museum, where the growth of a life form over time is shown in the same model.

Based on the above, the following is my firm belief.

The fourth-dimension of ‘higher space’ does not have to be geometrical. It can be time, which is perceived mentally. Therefore, all higher dimensions of space are, more likely, going to be perceived mentally.

Therefore, spirit (significance) shall contribute to higher dimensions of space, whereas, matter (mass) contributes to the three “geometrical” dimensions of space.

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