Space and counter-space are incommensurate principles. Counter-space is not space and space is not counter-space. In The OM Particle theory that I am developing, space and counter-space are not “places”, nor are they “spaces”. Instead, they are **domains**. Space is a “domain” and counter-space is a “domain”. The words “space” and “counter-space” are now just terms that I use to distinguish the incommensurate domains of a subject or system.

For example, when I say that the nucleus of the atom belongs to the *domain of counter-space* and the electron shells belong to the *domain of space*, I am using the terms “space” and “counter-space” as a teaching tool, to help to label the **incommensurate domains** of the atom.

From this list, you can see that I associate black holes with to the domain of counter-space and photon spheres with the domain of space. Dark matter belongs to the domain of counter-space and dark energy belong to the domain of space. The terms dielectric and permittivity belong to the domain of counter-space and the terms magnetic and permeability belong to the domain of space. Potential energy belongs to the domain of counter-space and kinetic energy belongs to the domain of space. Darkness and silence belong to the domain of counter-space and light and sound belong to the domain of space.

Now, hopefully, you can see the beauty in referring to space and counter-space as domains. The Principle of Incommensurability is the key to understanding The OM Particle Theory. To that end, I have adopted the terms “space” and “counter-space” as a teaching tool, to uniquely identify the incommensurate principles of seemingly dissimilar subjects.

Thus, in the cosmology that I am developing, you can’t say that counter-space doesn’t exist because counter-space is not a **thing** that can be proven or disproven. In The OM Particle theory, counter-space is defined as a domain. To say that counter-space doesn’t exist is to say that darkness doesn’t exist, or that voltage doesn’t exist or that potential energy doesn’t exist. The terms darkness, voltage and potential energy belongs to the **domain of counter-space** in The OM Particle theory.

In the case of the Mandelbrot Set (my muse), the central black region belongs to the domain of counter-space and the outer gradient region belongs to the domain of space. This is why the Mandelbrot Set makes such a great template for the Principle of Incommensurability. It serves as a nice visualization for the domains of space and counter-space, and more importantly, everything in between. What the Mandelbrot Set has taught me is that space is not important, and counter-space is not important. What is important is what happens BETWEEN space and counter-space. Looking at the geometry of the Mandelbrot Set, we find that the boundary that separates the domains of counter-space and space forms infinitely complex fractal boundary. Fractals happen between things. This is an important point.

*“Fractal geometry appears BETWEEN the domains space and counter-space.” FractalWoman*

A real life example of this can be found in this article called “Electrons on the Brink: Fractal patterns may be key to semiconductor magnetism”. This experiment demonstrates how electrons behave when a material transitions from a metal to an insulator. In terms of the Principle of Incommensurability, an insulator belongs to the domain of counter-space and the metal belongs to the domain of space. When the semiconductor is behaving more like in insulator, the electrons tend to clump together, that is, they behave more counter-spatially. And, when the material is behaving more like a metal, then the electrons are spread out over the surface, thus behaving more spatially. When the material behaves more counter-spatially, electricity cannot flow, but when the material behaves more spatially, then electricity can flow. But that is not the interesting part of this experiment. The most interesting part of this experiment happens at the transition point from metal to insulator. At transition, the electrons distribute themselves in complex, fractal-like patterns. This experiment demonstrates all the features of the Principle of Incommensurability as I am defining it. There is a counter-spatial domain, the insulator phase, and there is the spatial domain, the metal phase. And in between space and counter-space, we find self-similarity which is the signature of fractal geometry.

The other thing that I thought was interesting about this article is idea fractal geometry may be the key to understanding magnetism in semi-conductors. I won’t belabour it here, but you should read this article to find out more about the role the fractal geometry plays in the creation of the magnetic fields in semi-conductors. The experiment described in this article was a real eye opener for me in terms of the Principle of Incommensurability. This is when I realized that the terms space and counter-space are better defined in terms of domains. And, this is when I realized that I might be right about the fractal geometry of the Universe (or should I say OMniverse) after all.

So, when I use the terms “counter-space” and “space” in my teaching, whether they be videos or writings on my website, please don’t take the word “space” too literally. Sometimes it is meant to be literal and sometimes it is meant to be rhetorical. I will be sure to make this clear as we move forward.

*FractalWoman*