The Principle of Incommensurability

The Principle of Incommensurability plays a huge role in theOMparticle cosmology. If you can understand The Principle, then you will be able to understand me better too. The Principle itself is a kind of language. It is a meta-language that encompasses all the other languages. Computer scientists might call it a base class for scientific languages. Regardless of what it is called, “The Principle of Incommensurability” itself needs to be clearly defined. So let’s start with some definitions.

Principle:[prinsəpəl]: A fundamental truth or proposition that serves as the foundation for a system of belief or behaviour or for a chain of reasoning.

The Principle that I am proposing is not a theory, nor is it a model. It is a way of thinking. It is a chain of reasoning. It is my opinion that there is problem with modern cosmology. If the problem is with the language, then maybe we need a new language? If the problem is with the program, then maybe we need to rewrite the program. Maybe we need to redo everything from scratch? In the development of theOMparticle cosmology, I chose to do a complete rewrite, from first principles (i.e., from scratch). This new language forms the foundation for theOMParticle cosmology.

Incommensurability: [In-kuh-men-ser-uh-bill-uh-tee]: Having nothing in common, impossible to compare.

The best way to explain incommensurability is by example. Inside and Outside are incommensurate principles. Inside is not Outside and Outside is not Inside. Darkness and Light are incommensurate principles. Darkness is not Light and Light is not Darkness. Silence and Sound are incommensurate principles. Silence is not Sound and Sound is not Silence. As you can see, Incommensurate principles come in pairs, which brings us to the next important term in The Principle.

Conjugate:/ˈkänjəˌɡāt/: joined together, especially in pairs;  opposite, inverse or reciprocal yet coupled, connected, or related in some manner (conceptually related).

Incommensurate principles come in pairs that tend to be opposite, inverse or reciprocal of each other. I refer to this as the conjugate nature of incommensurate principles. Incommensurate principles come in pairs that are in conjugate relationship with each other (conceptually related, but opposite). Outside is the conjugate of Inside and vice versa. Light is the conjugate of Darkness and vice versa. Sound is the conjugate of Silence, and so on. This is how the pairing works.

There is one more very important aspect of “The Principle of Incommensurability” that needs to be explained and that is the concept of EMERGENCE.

Emergence : the process of coming into view or becoming exposed after being concealed. A revealing.

The concept of emergence in relation to The Principle is best explained by example using the famous Mandelbrot fractal, a universe in its own right. In a fractal universe like the Mandelbrot fractal, EMERGENCE is found BETWEEN the two incommensurate principles which I refer to as InnerWorld and OuterWorld. In the below figure, the dark inner region is InnerWorld and the outer gradient region is OuterWorld.

The Mandelbrot Set

That bright fuzzy region between InnerWorld and OuterWorld is where all the pretty fractal patterns live. This is also were all the interesting OMparticles live. In a paper I wrote called The Mandelbrot Set as a Quasi-Black Hole, I refer to this an an “event horizon”. This is where INFORMATION lives. This is where PHENOMENON lives. What I discovered through my research into the fractal nature of the Universe is that information (phenomenon) is always found BETWEEN two incommensurate principles. In my black hole analogy, I would say that information IS the event horizon of two incommensurate principles as depicted in the Mandelbrot fractal. It is my opinion that all “phenomenon” in the universe can be understood and EXPLAINED from the unique perspective of the fractal paradigm and the Principle of Incommensurability.

Below is a list a whole bunch of incommensurate principles that I collected over the years. The Principle of Incommensurability proposes the existence three distinct domains. Although they don’t officially have a name, in theOMparticle cosmology, I refer to them as InnerWorld :: OuterWorld :: EmergentWorld as depicted in the Mandelbrot fractal. To create the list, I divide all the important concepts I could think of into their InnerWorld-OuterWorld pairs. Once I was happy with that list, I went looking for the EmergentWorld term. The Principle is more than just a cosmology. It is a line of thinking. It is a chain of reasoning. It is a language. It is a philosophy. It is all of the above.

Now, I want you to forget “all of the above”. You will be able to gain a lot of insights into The Principle just by looking at this list. Each line contains three terms. first two terms correspond to the conjugate incommensurate terms and the last term is the emergent term.

Darkness :: Light :: Illumination

In the beginning was Darkness, and Creator said “Let there be Light”.

Light is not Darkness and Darkness is not light. Illumination is BETWEEN the two incommensurate principles of Darkness and Light. The concept of Illumination cannot exist without the concept of Darkness and Light. Without Darkness, what is being illuminated? Without Light, with what are we Illuminating? Between Darkness and Light are all the all levels of brightness and all the colours of the rainbow and beyond. In the beginning was Darkness, and Creator said “Let there be Light”. Illumination is BETWEEN the two incommensurate principles of Darkness and Light.

Silence :: Sound :: Hearing

In the beginning was Silence, and Creator said “Let there be Sound”.

Sound is not silence and silence is not sound. Hearing is BETWEEN silence and sound. If there was continuous loud sounds everywhere, you might not be able to hear me if I started talking. Hearing requires both silence and sound. Silence is the space between words and sentences. We need both silence and sound in order to communicate information. For example, Morse code requires both silence and sound to transmit INFORMATION. The silence between the dots and dashes is an important part of the information being transmitted. Similarly, the language of music has symbols for both sounds silence.

Noumenon :: Phenomenon :: Observer

In the beginning was Noumenon, and Creator said “Let there be Phenomenon”.

Noumenon is that which exists outside of the human senses a.k.a. that which cannot observed directly. Phenomenon is that which can be observed directly. Noumenon and Phenomenon are incommensurate principles. Observer is BETWEEN that which can’t be observed and that which CAN be observed. Observer is the interface BETWEEN Noumenon and Phenomenon.

Stasis :: Change:: Life

In the beginning was Stasis, and Creator said “Let there be Change”.

Stasis is defined as a  period or state of inactivity or equilibrium. The slowing or stoppage of the normal flow. Change is the incommensurate of Stasis and vice versa. Life can be found BETWEEN Stasis and Change. Life emerges from Stasis into Change and back again. This is known as they cycle of life. There could be no cycle of life, without the incommensurate concepts of Stasis and Change.

Stillness :: Motion :: The Cosmic Dance

In the beginning was Stillness, and Creator said “Let there be Motion”.

Stillness and Motion are incommensurate principles. Stillness is not motion and Motion is not Stillness. Motion is what happens when one comes out of state of Stillness. Stillness is the reference “frame” with which motion can be perceived and measured. The Cosmic Dance is what happens BETWEEN stillness and motion. I am talking about all the natural motions in the universe such as planetary motions and the motions of the galaxies and galaxy clusters and so on up the cosmological scale of OuterWorld. I am also talking about the motions of the cells, the atoms and the electrons and so on down the Quantum scale of InnerWorld.

Potential :: Kinetic :: Work

In the beginning was Potential, and Creator said “Let there be Kinetic”.

Potential is defined as having or showing the capacity to become or develop into something in the future. In other words, Potential represents future change. Kinetic is generally related to the motion of a material body (a body made of Matter). In The Principle, the terms Potential and Kinetic are incommensurate principles. Potential is not Kinetic and vice versa. But, in order to get work done, we need both Potential and Kinetic. Something must be stored (potential energy) before it can be released (kinetic energy) before it can do work. Potential is to Stillness qw Kinetic is to Motion.

Dielectric :: Magnetic :: Electricity

In the beginning was Dielectric, and Creator said “Let there be Magnetic”.

The concepts of Dielectric and Magnetic are incommensurate principles. Dielectric is not Magnetic and vice versa. Electricity is the “horizon” BETWEEN the concepts of Dielectric and Magnetic. BOTH concepts are required in order for Electricity to exist. Interestingly, the fuzzy event horizon region in the Mandelbrot fractal looks strikingly like electricity (pun intended).

Capacitance :: Inductance :: Resonance

In the beginning was Capacitance, and Creator said “Let there be Inductance”.

Capacitance and Inductance are incommensurate principles. Capacitance is not Inductance and vice versa. For example, capacitors resists change in voltage and inductors resist change in current. There are many incommensurate differences between capacitors and inductors. They are nothing like each other. However, both are required in order to build a resonant circuit. Resonance is an emergent property of the incommensurate principles of Capacitance and Inductance in relationship with each other.

Resistance :: Conductance :: Current

Resistance in a system is that which PREVENTS current to flow. Conductance in a system is that which ALLOWS current to flow. Resistance and conductance are incommensurate principles. Here, we could be talking about currents in a river, or currents in a circuit, it doesn’t really matter. With infinite resistance (no conductance) current cannot flow. With infinite conductance (no resistance), the current flows too fast. For current to flow at a reasonable usable rate, we need both resistance AND conductance.

Insulator :: Metal :: Semi-conductor

In he beginning was Insulator. And Creator said, “Let there be Metal”.

An electrical insulator is a material in which electric current does not flow freely. Metals are materials in which electric current does flow freely. Insulators and Metals are incommensurate principles. Metals are not Insulators and vice versa. Semi-conductors are BETWEEN metals and insulators. Semi-conductors are extremely important in the computer industry without which I could not be able to do my research or write in this blog. Interestingly, there is an article called “Electrons on the Brink, Fractal patterns may be key to semiconductor magnetism” which supports my idea that fractals can be found at the interface between incommensurate principles. In “Electrons on the Brink”, fractals appear at the TRANSITION point where a material transitions from a metal, to an insulator. In this example, this transition point or “phase transition” is the event horizon of two incommensurate states. So when I say the word “boundary”, I am not always talking about a 3-dimensional physical boundary. Sometimes, the boundary condition a critical point or a phase transition in a medium or material.

To be continued…

Voltage :: Current :: Electricity

In the beginning was Voltage. And Creator said, “Let there be Current”.

Sink :: Source :: Flow

In the beginning was Sink. And Creator said, “Let there be Source”.

Tension :: Pressure :: Force

In the beginning was Tension. And Creator said, “Let there be Pressure”.

Permittivity :: Permeability :: Medium

In the beginning was Permittivity. And Creator said, “Let there be Permeability”.

Absorption :: Emission :: Energy

In the beginning was Absorption. And Creator said, “Let there be Emission”.

In the beginning was Darkness. And Creator said, “Let there be Light”.

Charge :: Discharge :: Power

In the beginning was Charge. And Creator said, “Let there be Discharge”.


Radial Motion :: Circular Motion :: Orbit

Centripetal :: Centrifugal :: Spin

Scalar:: Vector:: Gradient

Convergence : Divergence : Emergence

Balanced :: Unbalanced :: Equilibrium

Contraction :: Expansion :: Resonance

Inaction :: Action :: Change

Permanent :: Temporary :: Transient

Homeostasis :: Evolution :: Life

Inert :: Active :: Live

Absolute :: Relative :: Relativity

Real :: Imaginary :: Complex

Mind :: Thought :: Imagination

Dimensionless :: Dimensional :: Fractal

Order :: Disorder :: Chaos

Stability :: Instability :: Self-organization

Inactive :: Active :: Cyclic

Infinitesimal :: Differentiatiable :: Calculus

Nucleus :: Electron Shells :: Weak Force

Formless :: Form :: Formation

Subjective :: Objective :: Observation

Confined :: Unconfined :: Free

Bound :: Unbound :: Liberated

Order :: Chaos :: Fractal

Dimensionless :: Dimensional :: Fractal Dimension

Unobservable :: Observable :: Illusive

Void :: Occupied :: Transition

Deterministic :: Predictable :: Chaotic

Incoherent :: Coherent :: Polarized

Continuous :: Discrete :: Quantized

Closed :: Open :: Circuit

Connected :: Connected :: Interconnected

Unknowable :: Knowable :: Uncertainty

Unknown :: Known :: Information

Unconscious :: Conscious :: Consciousness

Unaware :: Aware :: Awareness

Asleep :: Awake :: Dream

Emptiness :: Fullness :: Fulfillment

Dark Matter :: Dark Energy :: Visible Matter

Black Hole :: Photon Sphere :: Event Horizon

Soul :: Spirit :: Human

Creator :: Creation :: Creativity

Same :: Different :: Similar

Zero :: One :: Binary system

Introns :: Extrons :: DNA

Prokaryotes :: Eukaryotes :: Cell

Inseparable :: Separate :: Togetherness

Attraction : Repulsion : Magnetism

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