Page Created: 7/7/2015   Last Modified: 3/9/2016   Last Generated: 5/6/2024

Above/Below               Analog/Digital           Beginning/End       Hill/Valley
Compression/Expansion     Order/Entropy            Core/Surface        King/Peasant         
Structure/Detail          Construction/Destruction Efficiency/Waste    Energy/Matter
Birth/Death               Fast/Slow                Evolve/Regress      Hidden/Visible
High/Low                  Hot/Cold                 Idealism/Pragmatism Inside/Outside
Large/Small               Light/Dark               Presence/Absence    Circle/Line
Master-Slave/Peer-To-Peer Notice/Ignore            Old/Young           Rotation/Translation
Stimulus/Response         Fixation/Transformation  Unity/Separation    Vibration/Stability
Wave/Particle             Win/Lose 

The final clue that convinced me that the Universe is fractal was found when I was in the process of writing the screenplay for my film, Landmark. Up until then, I knew Nature contained fractal patterns, I knew that fractals could explain both our free will and determinism, but I never made the leap that everything is fractal until I started seeing fractal structure in thought itself.

After writing the first draft, I didn't know what I created, I didn't understand it, so I began to deconstruct it and discovered it was infused with dualism and binary oppositions↗.

I began to isolate a large set of, what I now refer to as, "Elements of Binary Opposition". There were so many of them, that I first began writing them on index cards, and eventually a wiki. Their presence convinced me that our "physical" existence is that of a dualistic being, that our thought and understanding of the world is one-dimensional, consisting of only 2 directions, like a double-headed spear.

I had applied deconstruction↗ to my own work, something I could not do until I completed the first draft, set it aside for a long time, and then examined it again with a fresh state of mind. You know the saying, a person that "wears many hats"? Well, that's when I first understood what it really meant, re-calibrating your own mind for a different task. Groups of people, working modularly and compartmentally, don't normally have to do this, as each person has their specialized task. But since I was trying to perform all elements of filmmaking as a single individual, I had to perform this re-calibration frequently, and my HyperSystemizing mind did not want to do this easily. It is extremely difficult to separate myself from my previous work and look upon it in a different way, even more so if the work is artistic or emotional.

In the early days, when I was still learning how to do this, I created systems for myself that didn't work--making huge checklists for the roles I needed to perform, even creating quite elaborate electronic checklists. One day, I decided that I needed to isolate physical space, and zoned off different desks and stations in my house for different tasks and labeled them, thinking that perhaps entering that space would force a limited context on my psyche, providing myself with only the tools for the task at that zone. I even thought about actually putting different hats at each station, literally wearing many hats...

It didn't work--this separation required the duplication of too many elements, it was inefficient, and it didn't impress on my brain the separation that it needed. When I was working on something, I couldn't get what I was working on out of my mind, the "obsession" component that people with OCD experience. I don't like forced transitions.

In school, I had such a difficult time switching to a new class each hour (since I was still thinking about my previous class), that I usually only caught the second half of the class material. But since much of this relied on what was said in the first half, my brain had to memorize abstract place-holders... and then later I would study and fill in the missing parts. This was tremendously uncomfortable, and so much of my schooling kept me in a daze, holding these abstract patterns. I fixated on those patterns that interested me, and the rest was fuzzy. For most of my 20's, I thought there was something wrong with my mind, as it did not have the acuity that it had when I was a child.

But after I turned 30, the acuity returned better than ever, like a fog that had lifted, as I had time to fill in all of those missing placeholders. And once this puzzle was complete, I realized that it was surprisingly simple, much less complex than the structure I had in place to hold all of that fuzziness. I was way overthinking the difficulty of the material, since by not knowing exactly what it was, I had allocated all of the resources I had to contain the enigma.

But while I had to deal with this difficulty in school, it had the unexpected benefit of boosting my memorization and abstraction abilities. My obsession led to a miscalculation, like the graph of an over-correcting system without proper damping, and it eventually converged back to a steady state. It is very common for one's deficiencies in one area to produce an advantage in another.

There are two hats that are the most difficult to wear. The most difficult transitions are the ones that required crossing empathetic and systemizing states. If I am empathizing, I cannot systemize, and if I am systemizing, I cannot empathize. I have to switch between them as if they are almost two distinct modes, as if each mode accesses areas of my memory that share very little in common with the other. This dualism is not unlike the dualism seen in human groups (War/Love or Science/Arts), and I would make a guess that the reason for this dualism in human groups is due to the same dualism inside of us.

I eventually learned not to fight this dualism, to work on the artistic or empathetic aspects when I felt like it, and work on systemizing ones when I felt like it, etc. My obsessions are thankfully self-limiting; they exhaust themselves when I begin to detect diminishing returns, a key to myself that a cycling phase is present.

I wore the hat that felt most comfortable at the time, and I approached my work with caution, knowing that other hat wearers were there before me. It is interesting that the halls of our own mind are just like the halls in a cave--we don't have access to the entire cave simultaneously, we have to traverse the space, traverse our mind, and this takes time. Our memories are elaborate constructions that we add to our entire lives. When we are young, they are convenience stores, when we are old, they are gigantic cathedrals with twisting labyrinths.

Everything we can comprehend can be explained by such a dualistic orientation. Even abstract concepts like Good and Evil are directions, binary oppositions. One would think that primitive directions would not apply the higher one goes into abstraction, but this is not the case. This is because that simple, 1-dimensional spear is moved to another area of a great fractal.

We simply orient this double-headed spear in fractal space. But the spear itself is not affected by this space, as it exists in space outside of the fractal, in Observer Space, like throwing a spear through a cloud.

I believe that all words that convey meaning have opposites. If they have no opposite, then they have no meaning. There may not be words for those opposites, but by using negation words and prefixes, they can be constructed. Some words are composites of many elements that have opposites. If a word has many opposites, then it has many subtle orientations, slight shifts of that spear, or synonyms.

I have always been critical of IQ tests for intelligence that ask one to match pattern or analogy from a collection of words or pictures. Many times when I encountered such questions, I could see numerous analogies, none more significant to me than the others. So what I had to do was to second-guess the test writers to put myself in their context to give them they answer they were seeking, pick the one that THEY probably thought was obvious, based on their own prejudices. Those kinds of tests are outright failures, and they test context more than anything else. You have to pre-load yourself with someone else's prejudices to successfully answer the question. I encountered this scenario over and over throughout my college years.

True/False questions were especially bad, inherently flawed, many of them containing loaded or subjective statements to which the teacher was oblivious.

A platypus is a large, egg-laying mammal. T/F

True: Incorrect, a platypus is a medium-sized egg-laying mammal.
False: Incorrect, a platypus is an egg-laying mammal.

What do they want to know, the animal's class, characteristics, or its relative size?

So when you try to compare binary oppositions, overlay them on each other to find congruences, you might find many, you might find that they don't match up right, like that awkward puzzle piece that you know is wrong but you still try to jam in place anyway.

But you might also find shadows of something real, something ghostly, a picture of something, a puzzle within a puzzle. As human brains have hurled billions of spears into this fractal universe, like beams of light, we have illuminated a scrim behind it.

Even binary oppositions, themselves, can be deconstructed, reduced to a very small set:

  • Separation (Rotation)
  • Direction
  • Magnitude

But this set, curiously, is not binary but tertiary. I have tried over and over to deconstruct this tertiary to a binary, but every time I did so, there was something missing. Dualistic worlds cannot be constructed from purely dualistic components. Even a Universal Turing Machine, while essentially binary, requires the missing element of energy. Without it, that special invention of Alan Turing, the pure decomposition of a digital computer, a magical device that can construct vast, realistic worlds from pure binary, will simply not move. It cannot move since is still a Machine and follows the Laws of a Machine↗.

The read-write head of a Turing Machine can be thought of as a "finite state automaton", like a boy with a shallow memory running back and forth along the Hollywood Walk, a long sidewalk paved with names, names he can only hold in his memory one at a time as he passes. But finite state automatons, or finite state "machines", have no concept of motion, or how that boy is to traverse those names. In other words, Turing's model of the computer is not complete, just like a schematic of an electric radio is not complete.

Such diagrams are "descriptions", written in a description language, structure only, a type of text-based schematic, analogous to InteractiveFiction versus a spatial RogueLike. Electronic hardware description languages, netlists, have no concept of Time, and motion, as we know it requires time. If one were to open up a cardboard box containing a new electric radio, that physical thing is merely a description, a description in 3-dimensional form, no less, written in plastic, copper, and silicon. But it does not really become a Radio until you plug it in and turn it on. At that point it transitions from description to the real thing, moving from denotation to connotation, becoming the 4th-dimensional entity that we are all familiar with, receiving signals from other places and other times↗.

This transition, this "breath of life", occurs in that mysterious gap between denotation and connotation. What is the difference between the living and the dead? If our heart were to stop beating, some would pronounce us dead. Notice the words used, "pronounce", or declare. It is not that one is dead, just that we are declaring one dead. Why? Because we don't have the certainty to make a statement of fact, just a statement of fact of our declaration. Even after thousands of years of civilization, we still don't know what delineates life from death.

What about the second or so between our heartbeats? Are we dead between beats, and simply come back to life again, second after second? What if that beat was our last one? Are we dead immediately after that last beat? Or do we have to wait for that mysterious brain death? And exactly when does brain death occur, when electrical activity stops? What if it resumes again?

In my opinion, death is simply description, something that is all around us but not really there, and life is the realization of that description, analogous to an epitaph on one's tombstone. The epitaph is the denotation; the life that fulfilled that epitaph is the connotation. They are performed in reverse order, however, but does that really matter? Free will and determinism are one and the same inside a fractal.

Separation is existence. When something exists, it becomes separate from non-existence, creating a dual, an anti-concept, and at its fundamental level, separation is both creation and destruction. When something that exists separates, it becomes a group, something separate from an individual, and this type of separation can extend into groups of groups, and groups of groups of groups, etc, like a tree bifurcating into complexity.

Separation is also dimension, degree of freedom. Separation creates our concept of space. We cannot envision things that separate unless there is a space between them, whether this is physical space or simply a construct in our mind (imaginary space).

And once space exists, we can apply the concept of direction. Direction does not have meaning in a dimension of 0, a point, only in a dimension of 1, a line. Separation, however, can turn that point into a line.

Whichever side of that line we focus on, we have oriented ourselves toward that side. This orientation is direction, like an auto-facing character in a roguelike videogame.

And while we are oriented, we may want to move closer to some of its far-away points, whether it is physical motion (requiring time) or simply our mental preference, moving our focus. This is magnitude.

But if all that exists is simply a Tree, and spacetime is an illusion, then we have no need for magnitude, since separation and direction are also movement. If we choose a direction at each point of separation, our focus will "move" through a tree, a quantized or stepped movement, from node to node, like traversing a graph database↗ or a packet radio network↗.

In mathematics and physics, magnitude and direction are combined into a geometric, arrow-like construct called a vector, but there is a hidden third component that is also represented, the dimension. Dimension, in vectors, is not represented by the length or direction of an arrow, geometry, but by more number positions, more placeholders, algebra.

In my opinion, this is a flaw in the construct. Vectors are not pure geometric constructs, they are composite constructs, but this is not clearly communicated to students of vector mathematics. When I first studied vectors in high school physics, I thought the concept was cumbersome, and I didn't understand their importance until I reached linear algebra.

Direction is a 1-dimensional concept that does not cross dimension. This is why projectile trajectory calculations must decompose the vector into its horizontal and vertical "components", as the perpendicular components of motion are linearly independent↗ (a.k.a "separate").

In linear algebra, there is a construct called a basis vector↗ which is exactly that--a vector which does NOT cross dimensions. The dimension theorem for vector spaces↗ states that dimension is simply defined by the number of independent basis vectors used in the space. In other words, our constructs are now sets of 1-dimensional arrows, each pointing perpendicular to each other. They do not have an analog direction, an angle, only the digital 1 to signify which dimension is theirs, but they do have magnitude.

However, unit vectors↗ are an opposite construct, vectors which cross dimension but have a magnitude of 1, and all larger magnitudes are simply multiples of these vectors. And just like me, some of them wear tiny hats↗ to indicate their role.

And finally, there is an even more primitive construct called standard basis vectors↗ which are a set of vectors that are both unit and basis (having both a direction and magnitude of 1 or 0). All of what we see in 3D space around us can be represented by collections of tiny, digital, 3-pronged arrows pointing at right angles to each other, like a bag of childrens jacks↗, a game of extreme antiquity, dating back to the ancient Greeks or earlier.

Like the read/write head on a long Turing Tape of 0's and 1's, magnitude is not present, as space on the tape is simple "jumped" as the program code branches. Could this jump simply be a rotation, a warping of that tape?

Separation is really just another name for rotation. Rotation is a "direction" that requires 2-dimensions, unlike direction, which requires requires just 1. You could say that rotation of a point particle, a zero-dimensional construct such as an electron, would not require additional dimensions, but this would not be rotation, for there is nothing to rotate, and subsequently point particles cannot be separated since they have no "parts". This is called "spin", but is very different than rotation, being discrete quantities described by extremely abstract constructs called spinors↗, and they cannot be explained by a bag of children's jacks or a spinning rubber ball, but by a tangle of strings↗.

To move a regular vector from the X-Y axis into the Z-axis, you simply rotate it upward, like lifting a spear in an arc toward a pouncing tiger. There is a unique coordinate system, polar coordinates, that simplifies such mathematics, relying heavily on Pi. And while dimensions in space seem to be independent, Pi, a mysterious, transcendental, irrational number arises out of a ratio of a 2-dimensional geometric length to a 1-dimensional one. Even 1-dimensional simple harmonic motion↗ that expresses Pi is not really one dimensional, but 2, requiring Time, since it is motion. Similarly, Pi itself cannot be computed algebraically, and any algorithm to generate Pi would require an infinite amount of Time. We know that spacetime is not flat due to Einstein's special relativity. Is Pi showing us a relationship between dimensions? Curiously, one of the most popular techniques for people that experience OBE's to separate one's self into an energy body is to "rotate" the body out of its physical body.

Rotation seems to be the material world's equivalent of oscillation in the world of energy.

Our observation seems to be a binary construction, a tree, but the observer is the one moving its focus along its branches. Note that while vectors can represent phenomena in space and time, they do not represent our point of view. When a person plays a 3D videogame, for example, everything they see on a monitor can be represented by sets of mathematical vectors, except one, the camera position, which requires a projection into the 2D space of the viewer.

While a binary tree of knowledge seems to be alive and growing in front of us, it has no meaning until we perform our interpretation, or pull an apple off of that tree.

Perhaps, for the fractal Tree, the physical world, there is only one element, separation, but for the observer, there is direction, or Choice. But, like the fire in Plato's cave, what mysterious lumination is facilitating this projection? Is this a third element, like the missing energy of Turing's machine? Perhaps we have perched ourselves, like birds, on a branch or "camera position" under a strange Sun where we can view this separation, since seeing the parts is the only way we can understand things.