*“Gravity exists. The sensation that we experience as gravity exists. To say that gravity doesn’t exist is like saying that life does not exist. Gravity exists. What doesn’t exist is an “explanation” for gravity.*

*FractalWoman*

Gravity is one of the most illusive “forces” of nature. Several questions surround the subject such as “Why does gravity exist?” and “Why does gravity only attract?”. Although we have a pretty good idea of what gravity does, the reason for its existence and how it came into being is still a big question mark. In this section, I will be using the Mandelbrot Set and the Principle of Incommensurability to help shed some light on gravity.

Put simply, gravity, and all **forces** for that matter, can be generalized as **gradients**. What is a gradient? In its simplest form, a gradient is a slope. The gradient of a slope is a measure of how steep the slope is. If the gradient is changing, that means that the slope is changing. The gradients depicted in topological maps, for example, show us how the gradient of a land mass is changing over some area. When the curved lines are closer together, it tells us that the slope of that land mass is steep. This might correspond to a hill. And when the lines are farther apart, it tells us that land is more flat and less hilly.

Now, I am going to show you something interesting about the Mandelbrot Set. It appears that the Mandelbrot Set is a kind of gradient generator. In the image (below) on the left, you can see a series of greyscale regions. The outer light-grey region correspond to one iteration. What this means is, it only took one iteration for these complex points to reach the “escape condition”. The next slightly darker region corresponds to two iterations and so on. As you get closer to the black region, you will find that it take more and more iterations to “escape”. The image below on the right shows a zoomed in region of the Mandelbrot Set. Here, I am only drawing the lines between iterations. As you can see, this looks very much like a topological map. And, as you can see, the closer the lines get to the black region, the closer together the lines appear, which in topology, would be interpreted as a steeper slope.

That said, instead of interpreting this as a topological map, we could instead, interpret it as a gravitational field map. In this analogy, I am now equating iterations with gravitational potential. The closer we get to the black region, the higher the iteration and indirectly, the higher the gravitational potential. Sound familiar? This is what lead me to believe that the Mandelbrot Set is a black-hole.

See: The Mandelbrot Set as a Quasi-Black Hole for more details.

Since the concepts of black holes and gravity cannot be separated, the Mandelbrot Set as as quasi-black hole, can be thought of as a gravitational potential generator. It generates all the “potentials” **at all scales.**

So, what does this all mean. What about gravity in the physical Universe? Fractals are still too illusive. Fractals only tell one part of the story. How can gravity be explained in physical terms, i.e., using physics? Well, to start this conversation, I need to invoke the Principle of Incommensurability. To really understand gravity, we must first understand the Principle of Incommensurability. Below are the incommensurate principles that will be used to help explain gravity.

## On Gravity

counter-space | space |
---|---|

dielectric | magnetic |

permittivity | permeability |

incoherent | coherent |

attraction | repulsion |

convergence | divergence |

connected | disconnected |

centripetal | centrifugal |

The Mandelbrot Set, as I see it, is the perfect template for the Principle of Incommensurability. First of all, the Mandelbrot Set literally lives in the complex plane, which in itself, embodies the Principle of Incommensurability. Second, when complex numbers are iterated through the through the function, Z := Z^{2}+ C, the complex plane gets divided into two domains, the domain of counter-space, and the domain of space. The central black region corresponds to the **domain of counter-space**. These are the complex points that **converge** toward counter-space when iterated through the function, Z := Z^{2}+ C. The outer gradient region corresponds to the **domain of space**. These are the complex points that **diverge** spatially when iterated through the function. The fuzzy boundary between the space and counter-space is a domain separator which I loosely refer to as an **event horizon. **It separates the **expanding** part from the **contracting** part. So, whenever I am talking about the domain of counter-space, I want you to visualize the inner black region of the Mandelbrot Set and whenever I am talking about the domain of space, I want you to visualize the outer gradient region of the Mandelbrot Set. In the Principle of Incommensurability that I am developing, space and counter-space are not “places” or nor are they “spaces”. They are better thought of as incommensurate DOMAINS. In this context, word “space” should not be taken too literally. **Space and counter-space are incommensurate domains. **

As you can see in the above table, the following terms are found in the counter-spatial column of the table: *dielectric*, *permittivity*, *incoherent*, *attraction*, *convergence*, *connected, centripetal*. All of these terms can be associated with gravity. Gravity makes things **converge** or come together. Gravity only **attracts**. The force that we call gravity is **centripetal** in that the force vectors all point toward the **center** of the gravitational body. Gravity is **incoherent** **dielectric** **attraction**, according to Ken Wheeler. We will talk about this in more detail shortly.

*“Counter-space is self-seeking and self-centring.” Ken Wheeler*

Of all of the things that I have heard Ken Wheeler say, this by far was the most striking and thought provoking. This, in my humble opinion, is the key to understanding gravity. The reason gravity exists is because the domain of counter-space is self-seeking and self-centring. This is the reason that gravity only attracts. This is the reason why gravity makes things “clump together”. **Self-seeking and self-centring phenomenon can only bring things closer together**.

*“All object in the universe are dielectric objects”. Ken Wheeler*

What he means by that is that all objects in the universe, including magnets, have a dielectric component. In fact, all objects in the universe have BOTH a dielectric component AND a magnetic component. The **dielectric** component is that which brings things together, and the **magnetic** component is that which keeps things apart. Yes, you read that right. Contrary to standard thinking, magnetic fields to not cause attraction. When magnetic fields are not present, then dielectric dominates and objects attract.

Although it is true that “magnets” do attract and repel, “magnetic fields” do not attract. Dielectric fields cause attraction and magnetic fields cause repulsion. The dielectric **lines-of-tension** are responsible for the sensation we perceive as attraction and the magnetic **lines-of-pressure** are responsible for sensation we perceive as repulsion. Here is an image that will help explain this.

In this image, you can see two sets of lines. The blue lines correspond to the **attractive-lines-of-tension,** and the red lines correspond to the **repulsive-lines-of-pressure**. As you can see from this image, the blue lines connect one object to another object, and the red lines come between and separate one object from another object. When blue dominates red, then the objects attract and when red dominates blue, then the objects repel. These are the only two fields that exist in the nature. All forces and phenomenon in nature can be explained in terms these two incommensurate fields. Although these two fields are orthogonal, and therefore cannot interfere with each other, they can, in conjugate fashion, interact with each other and affect the other. When the red (magnetic) field dominates, objects repel and when the blue (dielectric) field dominates, objects attract. This field geometry is what we perceive as as the electromagnetic field. In reality, it is a dio-electro-magneto-gravito field. All actions and interactions are a result of this field geometry. Both field geometries (red + blue) are required for the Universe to exist and persist. The Principle of Incommensurability demands it.

In terms of the Principle of Incommensurability, the blue attractive-lines-of-tension belong to the domain of counter-space and the red repulsive-lines-of-pressure belong to the domain of space. When red dominates, it **increases the space** between objects and when blue dominates, it **decreases the space** between objects. Attractive-lines-of-tension and repulsive-lines-of-pressure are incommensurate principles.

So, technically, a “magnet” is **MagnetoDielectric** object object. It both attracts and repels. It generates both repulsive-lines-of-pressure and attractive-lines-of-tension. The only difference between a magnet and a hunk of metal is, the magnet has been energized such that both the dielectric and the magnetic components have been exaggerated. The lines-of-tension are stronger and the lines-of-pressure are also stronger. That is why, in an energized MagnetoDielectric object, attraction is stronger and repulsion is also stronger. The incommensurability, which is normally only found at the small scale or atomic scale before energization, is scaled up to the scale of the magnet. In the language of the fractal paradigm, the energized magnet is said to be self-similar to an atom. So, what does all this have to do with gravity?

Ken Wheeler refers to gravity as **incoherent** **dielectric** **attraction**. In other words, it is the dielectric component of a material that causes them to come together. Dielectric lines-of-tension are counter-spatial. Wheeler says that counter-space is self-seeking and self-centring. If so, then it follows that materials with a dominant dielectric component should experience attraction. This is in fact the case. Here is a video that shows the self-seeking (clumping) nature of dielectric materials:

Longs story short, the astronaut(s) in this video took a bunch of materials like salt and sugar and coffee grinds, they put them into plastic bags. They shook them around… and then they observed. This, of course, was done in the microgravity of the International Space Station or ISS. Interestingly, many of the materials began to clumped together and, to the surprise of the astronauts, some of the materials clumped together **very rapidly**.

It turns out, the materials that clump together quickly are the materials with a high **dielectric** constant. Dielectric materials seem to clump together better. This is especially obvious in the microgravity of the ISS where all **other** **gravitational forces** are cancelled. It looks like Ken Wheeler is right when he says that counter-space is self-seeking and self-centring. The domain of counter-space, which includes such concepts as dielectric attraction and centripetal convergence, is the reason that gravity exists.

That said, I have to point out that “dielectric” is only one component or one “side of the event horizon” of the Principle of Incommensurability. The other side is the “magnetic” side. Materials that have a high dielectric component have a low magnetic component and vice versa. One does not exist without the other. When one goes up, the other goes down. There is no such thing as **permittivity** without **permeability**. Permittivity and permeability are reciprocals of each other. When permeability goes up, permittivity goes down and vice versa.

**Question:***What is the difference between a magnet and a gravitational object?*

* Answer:* According to Ken Wheeler, the main difference between a magnet and a gravitational object is field coherency. A magnet is a

**coherent**MagnetoDielectric object, and a gravitational body such as a planet, is an

**incoherent**MagnetoDielectric object. In coherent objects, such as a magnet, a good number of the atoms and molecules that make up the object have their counter-spatial and spatial domains aligned. Alignment of these domains amplifies field geometry such that, what is normally only seen at the molecular and atomic scales, can now be seen at the macro scale of the magnet. In other words, incommensurate field geometries have the property of self-similarity and thus, can appear at many scales, from the atomic scale right on up to the galactic scale. Galaxies are, for all intents and purposes, giant magnets. This is why galaxies have huge magnetic fields, and this is why galaxies have flat rotation curves. Galaxies are coherent MagnetoDielectric objects. This is why they “cohere”.

* Question*: What about globular clusters? Are they coherent or incoherent?

* Answer*: Globular clusters are incoherent MagnetoDielectric objects. That is why they have roughly spherical geometry. All objects in the Universe that have spherical geometry, such as suns, planets and moons, can be considered as incoherent MagnetoDielectric objects. Objects that exhibit polarization are considered as coherent MagnetoDielectric objects. That said, objects can be coherent, incoherent and

**everything in between**. Coherent objects can contain incoherent objects and vice versa. This is what makes the Universe so versatile and complex. Like the event horizon of the Mandelbrot Set, there are an infinite number of ways that space and counter-space can intersect. The patterns are infinite. The Universe need never do the same thing twice.

* Question*: There are some objects, like some asteroids and comets that are peanut shaped. How do you explain this kind of object?

* Answer*: Well, since these objects do not exhibit spherical geometry, I would have to hazard a guess and say that they are actually slightly coherent MagnetoDielectric objects. It is more coherent than it is incoherent. All objects are both coherent and incoherent. The degree of coherency will determine its ultimate shape.

* Question*: Why does gravity have an inverse square law?

* Answer*: That is a great question. This brings us back to the Mandelbrot Set. If we live in a “Mandelbrot” universe (

*as I am speculating*) then the inverse square law comes from the formula, Z := Z

**squared**+ C. In other words, a Universe that “squares itself” ends up with an inverse square law. In a fractal universe, all the laws of physics are generated via some iterative feedback process. What the Mandelbrot Set taught me is that inverse square law is more about the scale of an object and less about the distance between objects. A Universe that squares itself, will have an inverse square law appearing at many scales, including the atomic scale. Notice that the electrostatic force law, Fc, and the gravitational force law, Fg, both have in inverse square law:

Fc = * K*qq/r

^{2}

Fg = * G*mm/r

^{2}

It is my opinion that these are exactly the same law, only one is calibrated for small scale structures using the Coulomb constant, * K*, and one is calibrated for large scale structures using the gravitational constant,

*. In the fractal paradigm, the inverse square law is scalable. It is my opinion that, in order to unify physics, we must scale the laws of physics. This is what we appear to be doing here. Ken Wheeler says that all attraction has the same cause. All attraction is a counter-spatial, self-seeking and self-centring phenomenon. All attraction is dielectric in nature. All attraction involves the dominance of lines-of-tension over lines-of-pressure. Long story short, in a fractal universe, both electrostatic attraction and gravitational attraction have the same cause. The video from the ISS is a clear demonstration of this.*

**G**