The following is based on Ouspensky's idea of the six dimensions. Some say there are three or four dimensions, some say more dimensions (10, 11, and 26 are current favorites of some physicists), some say there are an infinite number of dimensions. But Ouspensky's explanation of the six dimensions resolves that dilemma by showing how six dimensions are both all-inclusive and yet only partial.
This entire area is at best only theoretical for me, but I find it gives me a valuable point of view in dealing with ideas of dimension, space and time. Ouspensky first developed his thoughts on the six dimensions prior to meeting the fourth way, but was later struck by certain correlations between the teaching of cosmoses in the fourth way and his thoughts on dimensions. He continued to develop and refine his theory of dimensions, but I know of no final conclusion, or even late summation of it by him. What follows is my understanding of Ouspensky's ideas on this topic.
We do not perceive our universe as it is—in six dimensions. With thought, to some extent, we can do that, and that is what this paper is about. In theory, we can develop consciousness to the extent that we are able to perceive the additional dimensions.
The fifth dimension, in Ouspensky's writings as I understand them, is the fourth dimension in infinite repetition. Here we can visualize it as the fifth dimension of space/time, in which the Frisbee solid (third dimension), moving along in time (fourth dimension), is repeated, or mirrored, in flights of infinite parallel Frisbees—infinite just as each of the previous successions in dimensionality are an infinite number of the previous dimension. But where do the infinite number of Frisbees come from?
If we look at the fourth dimension of space-time as the first dimension of time—the Frisbee as a point extended to describe a line—we now extend that line at right angles to itself to form a plane, the second dimension of time.
It seems to me that seeing the fourth dimension in this way leads easily to an idea of the fifth dimension, and one that is in line with quantum physics. If we see this tossed Frisbee as describing the fourth dimension, all other possible trajectories for the Frisbee represent the fifth dimension. This fifth dimension would then correspond to quantum physics' "superposition" in which, prior to measurement, a quantum system can be in any possible state or, rather, in all possible states simultaneously.
Finally, the sixth dimension of space-time, or the third dimension of time. The sixth dimension includes all possible expansions of the fifth dimension in space-time. Using the terminology of the three dimensions of time, the plane (second dimension), moved at right angles to itself creates a three-dimensional figure, but a figure in three dimensional time. It is actually a six-dimensional figure in space-time.
We can see the sixth dimension as the solid of the Frisbee, so to speak, that is as the point (the Frisbee) extended in time to become a line, repeated infinitely to become a plane which in turn is repeated infinitely to become a solid. This represents what Ouspensky called "all possibilities", in this case, for the Frisbee. But it is not all possibilities for an apple. An apple forms its own point, and line, and so on.
Now that summarizes the idea of the all-inclusive nature of six dimensions for any existence. But I said that this is also a partial dimensionality. This comes about because these six dimensions are relative to the point of view of the observer.
Back to our Frisbee, flying through space. An atom on this Frisbee could have no way of envisioning the Frisbee itself in space and time. It could, however, see itself in space and time. It could see that its continuation in time forms a line, and the infinite repetition of that line a plane, and the repetition of that plane a solid. That solid, all possibilities for the atom, is a piece, for us a point, of Frisbee.
The sixth dimension, all possibilities, is essentially the "multiverse" or "many worlds" interpretation of modern physics. The many worlds explanation is an attempt to explain observations of quantum phenomena that have no ordinary explanation but do have a consistent, but extraordinary, explanation. It basically goes like this: At every moment when you seem to choose among multiple possibilities, you actually choose each possibility, and different universes fork off, the one you are in now is the one in which you made the choice to read this, for example. There is another universe where you chose not to read this, another where you read part way and stopped and so on.
As the theoretical physicist David Deutsch writes as he is explaining the theory of parallel universes containing their own David Deutsch's:
"Many of those Davids are at this moment writing these very words. Some are putting it better. Others have gone for a cup of tea."
David Deutch, The Fabric of Reality
This is exactly Ouspensky's "all possibilities":
"Every moment of time contains a certain number of possibilities, at times a small number, at others a great number, but never an infinite number. It is necessary to realize that there are possibilities and impossibilities. I can take from this table and throw on the floor a piece of paper, a pencil, or an ash-tray, but I cannot take from the table and throw on the floor an orange which is not on the table. This clearly defines the difference between possibility and impossibility. There are several combinations of possibilities in relation to things which can be thrown on the floor from this table. I can throw a pencil, or a piece of paper, or an ashtray, or else a pencil and a piece of paper, or a pencil and an ashtray, or a piece of paper and an ash-tray, or all three together, or nothing at all. There are only these possibilities. If we take as a moment of time the moment when these possibilities exist, then the next moment will be a moment of the actualization of one of these possibilities. A pencil is thrown on the floor. This is the actualization of one of the possibilities. Then a new moment comes. This moment also has a certain number of possibilities in a certain definite sense. And the moment after it will again be a moment of the actualization of one of these possibilities [...] But all the possibilities that have been created or have originated in the world must be actualized [...] The sixth dimension is the line of the actualization of all possibilities."
P. D. Ouspensky, In Search of the Miraculous 
What Deutsch is referring to as "parallel universes" is what Ouspensky referred to as the sixth dimension, or "the solid of time".
"The quantum theory of parallel universes is not the problem, it is the solution. It is not some troublesome, optional interpretation emerging from arcane theoretical considerations. It is the explanation—the only one that is tenable—of a remarkable and counter-intuitive reality."
This section presents an analogy of six or seven dimensions—seven dimensions if the point or 0th dimension is counted as a dimension.
An analogy of dimensionality which originates in a point of existence and extends through space-time to include all possibilities for that existence:
The point at the apex of the shell represents the coming into existence. This is a point, a representative of no dimensions. The extension of this point is the first growth of the shell; it describes a series of points, i.e., a line, one dimension, extension in space. The line is next seen to curve, indicating the attribute of a next dimension which describes a plane—two dimensions, width and breadth. The curve is seen to spiral into the next dimension, indicating the three dimensions of width, breadth, and height. That this occurs over time indicates the fourth dimension, time itself. The motion over time now repeats to create the multiple spirals of the circle—repetition, the fifth dimension. The continual growth of the expanding spiral describes the ultimate shape of all possibilities for the periwinkle, analogous to the sixth dimension.
(Also see Qualitative Number Theory for related ideas.
A caveat. Ouspensky said:
"Every moment of time contains a certain number of possibilities, at times a small number, at others a great number, but never an infinite number. It is necessary to realize that there are possibilities and impossibilities."I agree that it is necessary to realize that there are impossibilities. As he goes on to demonstrate, he could not take an orange off the table (and you really must work with formatory thinking if you are objecting that he could). But I disagree when he says that every moment of time does not contain an infinte number of possibilities. I think it does. Surprisingly few people realize that infinite possibilities are not all possibilities. For example, the set of integers is infinite. But they are not all numbers. There are whole other sets of numbers that are infinite as well yet that are neither integers nor overlap each other. At this moment, I could type the next word or not, I could type it but misspell it, or spell it correctly, or I could misspell it with a number "1" in it, I could misspell it with a number "2" in it... or no*t.
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