Mandelbrot Fractal set: z <=> z2+c
“What I want you now to understand is that what you are doing now is simply remembering everything you are, and choosing the portion of that which you prefer to experience in this moment in this lifetime, on this planet, in this physical form. It is simple. You have separated your Self from the body of God, from the All, from the Collective, and you are becoming a member of that body once again. This is the Process called re-membering.” N.D. Walsch, Conversations with God, Book 3
‘As is the Human body, so is the Cosmic Body,
As is the Human mind, so is the Cosmic Mind,
As is the Microcosm so is the Macrocosm,
And as is the Atom so is the Universe.’
-Upanishads circa ~1000 to 500 BC“God said: And, yet, I have said there is no distance. There is no close-up. I have said there is no time to speak of. We could say, as a manner of speech, that you and your supposed life are encapsulated in one moment.” HL 4838
Is the Universe a Russian nesting doll?
Circa 1984, the French mathematician Benoit Mandelbrot was searching and did find a unitary mathematical formula that would express the extreme complexity of roughness (for example, a landscape, a coastline) through order patterns that seem very complicated. This mathematical formula [z <=> z2+c] is at the foundation of what is now known as fractal maths and as the Mandelbrot fractal set. The symbol “< = >” means that the equation is recursive, namely, that is each term of it (z) is determined by the application of the formula z <=> z2+c to preceding terms.
Fractal like fraction means literally “broken into pieces” from Latin “frangere, fractum”, to break. A fractal (as can be seen on the header picture of this blog) is a geometric pattern that is repeated indefinitely at ever smaller scales to produce irregular shapes and surfaces that cannot be represented by classical geometry. Computer modeling of irregular patterns, shapes and structures occurring in nature — even the shape of organs like the brain, the lungs, the neurons, etc. — is based on fractal maths. Fractal sets are now used as a unifying equation/theory in neuroscience to explain the structure and function of the brain and even as a unitary model of the universe. Mandelbrot’s fractal equation has the same kind of unifying impact as Einstein’s equation E=mc2 unifying energy and matter.
One of the most eloquent contemporary researchers and spokesmen applying fractal maths to neurological research is Wai H. Tsang, who promotes the Fractal Brain Theory as the unification of neuroscience with artificial intelligence (AI), psychology, metaphysics, and cosmology.
Wai H. Tsang made the statement that the Universe is built like a Russian nesting doll. The Russian nesting doll is a simplified representation of a fractal object; that is an object that has the following property: the structure of its constituent parts reflects the structure of the whole and at various scales. It is very closely related to holography. In fact, we find the same relation between a fractal set and a hologram that we find between space and time. They are a reflection and determination of each other or, otherwise said, they are just two different perspectives of a unique phenomenon. Russian nesting dolls are also analogous to the wiring patterns common across worm brains, human brains and computers (binary trees). Just think of the nested folders on your computer’s desktop.
Wai Tsang’s basic idea behind the Fractal Brain Theory is that the brain is a fractal computing architecture working through the properties of symmetry, self-similarity in structure and process, recursivity and feedback loops. The process of fractal computing lies on rotation, translation, scaling, scaling and rotation, and reflection. This reminds us of how the brain system of vision works in the neurological process of inverting and recombining two half images to supply us with a proper right-side up, symmetrical, complete image of an object of the external world.
A natural representation of a fractal is the structure of a broccoli or cauliflower. The whole broccoli looks like a tree and is composed of several smaller trees which are composed of even smaller trees. This is the self-similarity property of a fractal object. And this self-
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similarity is dynamically expressed, through the process of scaling, by its nesting structure. The smaller constituents that make up the whole also reflect the whole and they are composed of even smaller constituents that are smaller copies and reflections of the whole. This process can potentially go on ad infinitum.
Is there a continuity between the brain and the mind?
The fractal theory of the brain postulates a continuity between the brain structure and its functioning. The whole brain behaves structurally and functionally as its fractal part replica. A neuron will share the same arrangement and functioning as the neuron complex. A fractal network, by the very fact of its self-similarity, branching system, recurrent connection between inwards and outwards branching (like the root and the branch system of a tree), will create unity, communication (by feedback), and togetherness between the parts and the whole. We find a similar continuity between the structure and function of language through verb phrases, noun phrases, concatenation, and, at a global scale, the nested patterns of thoughts. At an even higher level of abstraction, we could talk about the storage of knowledge itself…
In one of his public presentations in 2012, Wai Tsang said:
“We further propose that this fractal structuring of the brain and self-similar way of conceptualizing its organization and functioning, derives from a recursive generative process which is a property of many fractal structures generally. This recursive process starts from a seed or atom of recursion, and through it all brain structure emerge…
… this Atom of Recursion or Seed of Brain and Mind may potentially exist, because all biological forms derive from the recursive bifurcation process of cell division starting from the fertilized egg. We believe that the process of the brain and the process of thought can be conceptualized as a continuation of this process of ontogenesis and also neurogenesis, i.e. the production of the physical substrate of mind.”
It then becomes easy to extrapolate that understanding the arrangement and functioning of the brain leads to understanding the arrangement and functioning of the Universe itself in a self-similarity pattern. This does not mean, for Wai Tsang, that consciousness in the Universe is only an epiphenomenon of the fractal brain, or more globally speaking, of physical matter. On the contrary, he believes that existence is really consciousness and that the idea of the fractal brain structure serves to reduce all existence to a Single Consciousness. He sustains “This approach works together with the idea that the physical Universe is illusory and that what is behind the illusion is mathematical or platonic existence.”
The idea of continuity between the structure and functioning of the brain and the structure and functioning of the universe leads to the idea that there is a Single Consciousness [God] that makes a subjective experience of itself through the illusory physical universe. That Consciousness breaks itself into parts (fractals) at various scales of the universe and experiences itself simultaneously at all levels and scales but as apparently discontinuous individual subjective lives and experiences, each life creating its own space and time, yet being linked to the whole at all levels and scales through recursivity and feedback loops.
However does the fractal unitary model of the brain and the physical universe ascertain the continuity between the brain and the mind, and, by extension, does it achieve the reconciliation of (neuro)science with spirituality? Wai Tsang believes it does.
The magical thinking behind the fractal brain metaphor
In the preceding blog (#60 Magical Thinking and Right-Mindedness 1: Healing), we said that, in our medical thinking, we were facing three choices of belief: 1) only the body is real; (2) both the body and the mind are real, and 3) only the mind is real. If we accept that Perfection is the principle behind healing, then we can no longer confuse the mind with the body and, by extension, the mind with the physical universe.
If we apply the Principle of Perfection to the Fractal Brain Theory, we have to ask ourselves if recursivity, as we conceive it in fractal maths, is the real principle behind consciousness experiencing itself continuously, but at the same time at fractal ( broken, fragmented) scales or levels. In other words, does the Mandelbrot fractal set preexist in the universe as a platonic idea? Does Consciousness, Oneness [God], create images of Itself through an atom of recursion that proceeds by recursive bifurcation (like cell division)? Is being created in the image of God equivalent to say that we are a fractal or cloned piece of God at a different scale?
If One is indivisible, it cannot really divide itself, it can only multiply and extend itself in infinity and eternity. And it multiplies and extends itself multidimensionally, not only scalarly. Here is an illustration.
Is a snowflake a real fractal? The difference between Sameness and sameness
No two snowflakes are alike. Snowflakes are not clones of 
each other no more than a grain of sand is a clone of the other grain of sand no matter the scale. All fractal snowflakes, generated through computerized fractal modeling, are clones. They look identical, they are self-similar at all scales, yet they don’t have any real identity. Their sameness is recursively redundant. A real identity is a singularity, and each natural snowflake is a singularity. SINGULARITY is not expressible in any conceivable mathematical formula or equation. It cannot be really represented, only known and experienced. Perfection is a singularity because it IS Oneness. Perfection is the real Sameness without redundancy or recursivity. We are all singularities coexisting in the Singularity of One [=God]. This is a mystery, namely a secret revealed to us by closing the eyes. Perfection in Sameness is the DIVINE DICHOTOMY. Sameness and Perfection are synonymous. Sameness is the principle that generates the vibration of Love, and Light is the Silent Vibration of Sameness as a response or echo to Love. Light is linked to the recognition of Sameness by remembering Perfection. This is the return to right-mindedness.
Unitary mathematical equations are non-creative agents just like medication
This is a crucial point to make when we are considering unitary mathematical equations as Einstein’s E=mc2 or Mandelbrot’s z < => z2+c. In mathematics, an equation is a statement that the values of two mathematical expressions are equal (the = sign). It is the process of equating one thing with another or saying that two things are the same, using mathematical symbols.
If we take Einstein’s E=mc2, we will mathematically say that energy is the same as matter accelerated to the square of the speed of light. But if the two members of the equation (respectively to the right and to the left of the equal sign) were the same or equivalent, then it would allow to conversely transform that same energy into matter. Yet this equation empirically allows only to transform matter into energy (with residues also called wastes). There is no real adequation or equivalence.
This is the underlying magical thinking behind unitary mathematical equations (see blogs #41-42 An Eye for an I). A unitary mathematical equation is an equation that can supposedly define the totality of physical reality, assuming that the universe is a mathematical entity. It defines sameness on the basis of mathematical belief that either 1) only the physical world is real; 2) both the physical world and the mind are real; 3) only the mind is real. Mathematicians seem to oscillate between those three beliefs. But implicitly, mathematicians believe that only the mathematical (platonic) mind is real. Is God a mathematician? Yet they are trapped in their belief because of the impossibility inherent to a unitary equation to express singularity.
It follows that unitary math equations are not and cannot be the principle underlying and leading the Universe, but they express a mathematical process led by the Perfection Principle and the result is a SINGULARITY. By themselves, they can only generate recursive and redundant sameness (clone) which has no life of its own. Only life can generate life, and each life is a singularity. Life as a creation of Sameness is itself a Singularity of singularities. That is also why mathematical equations are non-creative agents just like medication. But like medication, they are utilized as a compromise approach to the mind and the physical world, in which something from the outside (mathematics) is temporarily given a knowledge healing belief. Here again we find that confusion between a principle, a process, and a result.
The wiring pattern of the cerebral cortex: a 3D grid?
The wiring of the cerebral cortex, at first sight, resembles a fiber bundle (see illustration at the right). But, with the aid of scanners of incredibly high resolution, neuroscientists have been able to peer into the brain and discover that the basic structure of neuronal networks was a simple 3D grid. The pathways cross perpendicularly (90° angle) to form checkerboard-like, 2D sheets. These 2D sheets form a 3D grid by stacking up along adjacent 2D sheets.
Van Wedeen (of the Massachusetts General Hospital’s A.A. Martinos Center for Biomedical Imaging and Harvard Medical School) says “Brain wiring is not like the wiring in your basement, where it just needs to connect to the right endpoints. Rather, the grid is the language of the brain and wiring and rewiring work by modifying it.” This means that the grid serves as a template for the growth of the brain from its embryonic to mature stage and the rewiring occurs constantly through the genetic and environmental influences.
But how can a checkerboard-like grid or matrix of nerve fibers be the language of the brain? Neuroscientists try to understand the way in which the brain provokes the precisely coordinated activation of distant neurons. Here, the temptation is very strong to “reduce” the mind to a set of operations executed by the brain and see the mind as a magnetic “cloud” resulting from the electrical activity of the brain. Can the simple mapping of the 100 billion neurons constituting the brain structure lead to the understanding of its function? Can the mapping of the complete human genome (including the so-called “junk” DNA) lead to our understanding of DNA function? Magic thinking seems to be still at work in most main areas of scientific knowledge.
3D perpendicularity and orthogonal quantum states
What is the real meaning and purpose of a neuronal wiring where the fibers intersect at right angles (90°)?
To postulate a continuity between the mind and the brain implies that orthogonal intersections (90°) are existing in the same plan or dimension (2D or 3D). Our perceptual apparatus makes us believe that solid matter is built with intersecting lines (nailing vertical and horizontal beams at 90° angles to build a 3D house, for example).
But if we introduce once more the Principle of Perfection, we will be led to think that a network, a grid, a matrix is a multidimensional object. Instead of thinking that perpendicularity occurs in the same plane or dimension, let us imagine an orthogonal quantum state. The concept of orthogonal quantum states can be summarily presented as follows. It is known in quantum physics that a photon with a vertical polarization will never pass a test for horizontal polarization (and vice versa). In terms of vectors, it is said that vertical and horizontal polarization are two orthogonal (90°) quantum states of a photon. “It is a remarkable property of photons that any other single-photon polarization state can be formed from a suitable linear combination of vertical and horizontal (polarization) states, possibly with complex coefficients. We say that single-photon polarization is a two-state (or two-level) quantum system and that vertical and horizontal form a basis for the space of polarizations (an example of a Hilbert space). [Source: Los Alamos National Laboratory].
This sounds a little bit technically complex and it is, yet it has the extreme simplicity of the Divine Dichotomy. It puts into light the fact that there is no real linear continuity in the same plane or dimension between the mind and the brain. It is more of an orthogonal quantum state led by the principle of Sameness and reflected in the matrix of the neuronal wiring. And from a Perfection and Sameness perspective, it makes a lot of sense.
Quantum orthogonality is the process of the Divine Dichotomy of Sameness in Perfection. The quantum vertical polarization of the neuronal grid is our vertical connection to who/what we are in the Eternal Present Moment. The quantum horizontal polarization is our space-time connection to who/what we want to be. Rather than passing through different fractal structures, the One Consciousness oscillates or vibrates between the states of Perfection and Sameness. We write our personal life scenarios (present and parallel lives) in a horizontal sequential time-space framework within One vertical Moment. God says: “And, yet, I have said there is no distance. There is no close-up. I have said there is no time to speak of. We could say, as a manner of speech, that you and your supposed life are encapsulated in one moment.” Vertical synchrony meets horizontal diachrony. Everything is happening all at once. We just have the impression or illusion of passing by and through fractal structures or more exactly through multiple singularities in a space-time framework. The brain is a device that allows God to experience His Singularity through our own singularity by going through the process of forgetting and remembering in an embodiment condition. Quantum orthogonality is what makes this experience possible. The brain processes Light through its orthogonal quantum matrix. Love through Light is the principle, the process, and the result of that matrix. It is the language of this matrix.
Holographic scenarios for the game of life
If the neuronal grid or matrix is the language of the brain, then the orthogonal quantum state of our neuronal network carries the purpose and meaning of that language. In order to experience what it feels like to be God, we accepted to take an embodied human form. But our soul was never imprisoned in a body. The body does not contain the soul. It is the soul that contains the body. This is how it is possible to remember when we forget. If the soul were totally contained in the body, it would not be possible to remember. The body is the device that allows a portion of our consciousness to forget in order to insert itself in the time-space continuum of the physical “reality”. This can be represented by the horizontal polarization of the photon in the orthogonal quantum state. But the core of what we are, our real and eternal essence, is always in the eternity of the Present. And this is represented by the vertical polarization of the photon in the orthogonal quantum state. It is as if we exist in two places at the same time, heaven and earth. One place does not have any time and space coordinates while the other one has. And those two “places” are perpendicular to each other.
In order to imagine and play a game or a scenario of life, a certain reality of choice has to be created. We cannot be something without not being something else. So in order to make the choice of who we want to be in a space-time framework, we have to forget the eternal Present of who we really are. In the orthogonal quantum state, it has been said that a photon with a vertical polarization will never pass a test for horizontal polarization (and vice versa). This puts into light that there is a sort of mutual exclusiveness between two states of the same photon (vertical and horizontal polarization). Forgetfulness and remembering have that orthogonal quantum state relation. And it has to be so in order to create a state of forgetfulness that allows choice. Since energetic particles can be expressed by their frequencies, exclusiveness is also energetically expressed by a frequency. This frequency is the frequency of the color black. This frequency of black is what allows “negation” that renders “affirmation” possible. Its equivalent in the world of numbers is zero.
The neuronal grid, combined with all the other nested neural grids of the Universe (or universes) creates an environment to elaborate imagined scenarios that are like computer programs. These programs can contain entire civilizations since all the neuronal grids are nested. These programs are sentient because they involve physical, emotional, mental, and spiritual experiences through thoughts, feelings, and actions. This also involves not only the memory located in the brain, but the memory stored in our physical and quantum DNA.
We are just on the verge of fantastic discoveries, as long as we abandon the fear of leaving our linear, sequential thought process.
Written by Normand Bourque on Feb 21, 2014
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