First we have to think, what is a negative dimension. We pretty well know that at least two have to exist to have topology and geometry. If one or two are needed there is nothing preventing all the others from existing. We know what positive dimensionality is because we live in it. And we can just extend that upward to higher dimensions. My General Schemas Theory proposes a relation between schemas and dimensions such that there are two schemas per dimension and two dimensions per schema. The schemas are ten in the S1 hypothesis and they cover dimensions -1 through 9. (http://emergentdesign.net) Now the lowest schema is the facet, which is below the monad. Each higher schema has an expanded scope. The facet is like quarks that are never seen apart. Facets have -1 and 0 dimensionality while monads have 0 and 1 dimensionality. So monads can be strings and not just zero dimensional points. If a facet is zero dimensional then the monad that it is part of needs to be one diFirst we have to think, what is a negative dimension. We pretty well know that at least two have to exist to have topology and geometry. If one or two are needed there is nothing preventing all the others from existing. We know what positive dimensionality is because we live in it. And we can just extend that upward to higher dimensions. My General Schemas Theory proposes a relation between schemas and dimensions such that there are two schemas per dimension and two dimensions per schema. The schemas are ten in the S1 hypothesis and they cover dimensions -1 through 9. (http://emergentdesign.net) Now the lowest schema is the facet, which is below the monad. Each higher schema has an expanded scope. The facet is like quarks that are never seen apart. Facets have -1 and 0 dimensionality while monads have 0 and 1 dimensionality. So monads can be strings and not just zero dimensional points. If a facet is zero dimensional then the monad that it is part of needs to be one dimensional. But if the monad is zero dimensional then the facet must be -1 dimensional. And this dimension is the gateway into the imaginary numbers, thus imaginary dimension. So there are really two things below the zeroth dimension, negative and imaginary dimensions.

Now it is pretty obvious that there are no objects in negative dimensions. There is no one looking at any objects because there is no separation between things in negative dimensions. Rather we have “embeddings”, like the science fiction book of that name by Ian Wallace. The higher the negative dimension the deeper the embedding. It is like the implicate order that David Bohm talks about. So a point has a facet if there is superposition. The superposition is an embedding in negative dimension. The same point has multiple independent states at the same time with out them mixing because the negative dimensionality allows them room to exist embedded in each other. If two things are in a pure state (probability wave) together and then they are separated they keep that embedding and that becomes entanglement. So here we are proposing that superposition and entanglement are the two outward manifestations of embedding in negative space.There can be multiple states that overlap within an embedding space like first negative dimension one. This overlapping takes up no space.

Plato in the Timaeus talks about both the chora and the receptacle. The receptacle is something like normal empty space, i.e. the Void. But the chora means places in the receptacle, and so we might call these separate embeddings chora. If we have negative one dimensional chora then that is the negative dimensional inverse of the line. That is stackable embedding places. But each place is only at the trace level, and there is not an actual space associated with it. There is only a set of possible infinite stackable facets that can be together overlapping without taking up any space of the positive variety. If we can think linear embeddings then we can think any dimension of embeddings of chora.

But if we do the equivalent of a square root of the negative dimension then we can also get the symmetry breaking that would provide access to imaginary dimension. What is interesting is that imaginary dimension cannot be thought either, but we have no problem representing the two dimensional complex plane. So why should we have more difficulty with negative dimension when we have no problem with the imaginary numbers which clearly open up their own odd dimensionality.

Now here is an idea, which is that it is imaginary dimensionality is time. This would make time orthogonal to space, and it would mean that various orthogonal timelines would exist such as those that appear in F theory in the 12th dimension, would also explain why Dunne was right about the multi-dimensionality of time. They are just not real dimensions but imaginary ones. It then becomes interesting so we can see how negative dimensionality plus imaginary time might give us the actual experience we have of timespace.

I differentiate spacetime from timespace (Minkowoski) and call both together the Matrix (even before the Matrix movie came out). Spacetime is an interval which seen from different viewpoints have different phase space divisions between time and space based on different reference frames. Timespace on the other hand sees things in terms of causality and worldlines and identifies an unreachable region where light cones cannot overlap. These are two views of the same thing, the Matrix. Now if time is multidimensional and imaginary then it is conjuncted with space and that is like timespace. But this does not produce the phase transitions from different frames of reference we see in spacetime. This is where negative dimensionality comes in. Negative dimensionality allows time to be embedded in space, not just conjuncted with it. No one seems to ask where the different phase spaces seen from the different frames of reference are stored. The different frames of reference are embedded in negative space. They are essentially global chora. All the different phase space transitions between space and time in spacetime are embedded together in negative space. Thus time appears in two simultaneous actions that bring together imaginary and negative space. Negative space is the effective space of Quantum Mechanics as well because it can explain the two main phenomena of superposition and entanglement with one concept embedding.

Anyway, all this is to say, that what is in negative dimensionality and imaginary dimensionality are not objects but rather traces and propensities related to the various kinds of Being.

copyright 2011 Kent Palmer

http://www.quora.com/What-would-an-object-with-negative-dimensions-look-like