A Simple Explanation of the Multiverse--"What is possible is actual"

My brother, Bill, and I have been kicking around the implications of an infinite set of multiple universes. The discussion began with his discomfort over the many-worlds interpretation of quantum mechanics--that infinite multiple parallel universes branch off from every random quantum outcome of our universe. 

My reply was that it didn't bother me to think of infinite dimensions branching off of what we call reality, because the metaverse is infinite, and we rest inside of it, so there's plenty of room, so to speak. Also, since there are infinite dimensions wrapped around us, any point in our universe can map outward wherever it wants to go.

After a couple of days and a couple of phone calls, Bill called me all excited after experiencing an Insight. "Modal logic!" he declared. Then he proceeded to tell me many things about modal logic that I barely followed, because I majored in Rhetoric rather than Philosophy. (I manipulate words and diagrams as symbols, while he is comfortable manipulating logic and math symbols.) 

Once he started speaking English again, Bill said, "Modal logic talks about possibility and necessity. I realized this morning a new proposition that answers our inquiry! It's: 'What is possible is necessarily actual under an infinitely many-worlds interpretation of quantum mechanics!'"

We humans say it all the time: "What can be done will be done." As if it were a universal law. And of course it would be a universal law, because it's a fractal meme, isn't it? After all, if it can be said, it has been said--again a universal fractal meme.

If the universal consciousness thought up the algorithm that became our bounded universe, and that originating consciousness is infinite and illimitable, then there is a necessity for the infinities of consciousness, time, and space to be expressed in infinitely branching possibilities. 

This interpretation fits nicely with the many-worlds interpretation of quantum mechanics and complements string-theory notions of Hilbert space.

Read the Simple Explanation of the Fractal, Conscious Universe here.

A Simple Cosmology of the Universe

Before the beginning, before space and time, there was nothing but pure consciousness. And consciousness had neither pattern nor form, only awareness.
The Simple Explanation calls the pure consciousness that exists outside our universe the “metaverse.” In the original Greek, “meta” means an idea above and beyond the topic of discussion that brings greater understanding and context to the topic. In this case, the topic is the nature of the universe. In order to better understand our universe, the Simple Explanation begins with that which lies beyond this universe—the metaverse. This metaverse has many names in many traditions—“The Great ‘I AM’” and “God the Father” in the Torah and Bible, “Sat” and “Parambrahma” in Hindu scriptures, the “Tao” and “wu ming” in ancient Chinese texts, and “The Absolute” in modern philosophy.

Then consciousness had a thought which unfolded into countless dimensions. This multi-dimensional metaverse still lacked space and time but it now quivered with limitless mathematical potential. In a twinkling, our entire universe was imagined in the fullness of its complexity, from the tiniest quanta through the greatest astral body; every animal, vegetable, and mineral; every element; everything. At the moment this thought occurred, the metaverse conceived every organizing principle needed to shape and sustain space and time, energy and mass. All was in ideal balance. Every system was theoretically in tune; every function perfectly performed; the consequence of every action anticipated, understood, and plotted to the nth degree. And it was all good.

Once the metaverse formed a particular thought, thought became an object in the great sea of no-thought. Where there was only pure consciousness, now there existed something—thought. In order to preserve the undisturbed tranquility of the metaverse, thought sealed itself off from pure consciousness by focusing inward, and in so doing formed a toroidal-shaped bubble around itself. Where there was only the tranquil nothingness of the metaverse, there was now thought and directed action, initiating sequential time. On this day that time began, consciousness wrapped itself around our universe, forming a border between us and infinity. Mind took on a shape.

The “Shape of God’s mind,” also known as  the “Universal Unit of Consciousness,” the “Womb of Creation,” the “Son of God,” “logos,” “the Word,” the “universal fractal formula.” We can think of this wireframe version of the toroid as the idealized mathematical blueprint imagined by the metaversal consciousness prior to creation.

This toroidal-shaped membrane is composed of conscious thought and its concept of this universe, split off from the unformed metaverse and operating on its own. The Simple Explanation calls this original torus the Universal Unit of Consciousness (Universal UC). The content of its thought is the entire logos of our universe. The Bible puts it this way:“In the beginning was the Word, and the Word was with God, and the Word was God. Logos was in the beginning with God. All things were made through the Word, and without this logos, nothing was made that was made,” (John 1:1).

Which begs the question: How is it possible for an object (our universe) to rest "inside" the formless metaverse without affecting its undifferentiated nature? How can space and non-dimensionality, time and timelessness, change and the changeless co-exist without touching the untouchable metaverse?

This paradox is easily solved by imagining that the toroidal membrane itself possesses a fractal surface akin to the Koch snowflake. As you can see, through endless divisions, the perimeter of the figure becomes infinitely complex and long, while the interior of the 2-dimensional Koch snowflake remains finite and contained to the figure, never reaching "outside."



These are the first four iterations of the Koch snowflake fractal formula. At each computation, a side is divided into three equal segments and an equilateral triangle the length of a segment is placed at the center segment. The center segment’s line is then erased, leaving behind a perimeter that is four times longer than the original side. Even though endless computations may lengthen the perimeter to infinity, the snowflake’s volume remains finite.

Now imagine applying the Koch divisions to the surface of the Universal UC torus, with the divisions facing outside. As the membrane divides toward infinity, the space within remains finite and contained; keeping the undifferentiated unity of the metaverse unsullied. The effect of this infinitely recursive fractal surface can be likened to that of an invisibility force field deployed around our universe, i..e, "What happens in our universe, stays in our universe."

The concentrated thought of the Universal UC focused inward on a singular point of limitless energetic potential—enough to seed our universe. Concentration gave rise to toroidal forces that begat energetic waves. Our universe began to expand outward as energy exploded into the torus of space out of the zero point field at the center. In Sanskrit, “ananda” means both energy and joy. The Simple Explanation suggests that organized consciousness , “chit,” combined with ananda and began emitting the building blocks of our universe.

Shape gives rise to toroidal forces that explode into dimensional space as patterns of energy culminating in material quanta.  Cosmologists refer to this initial energetic event as the Big Bang.

 

As the interior torus of our universe expanded, over and over and over again pale echoes of the Universal UC attached themselves to the particles streaming out of the Big Bang. In Sanskrit, these smallest material quanta are individually known as “anu” and collectively called “maya,” or creation. “Avidya,” Sanskrit for “loss of consciousness” or “delusion,” is a necessary by-product of material instantiation as each individualized point-of-view in time and space replaces universal, non-localized awareness.

The Universal UC pulses with concentration at the birth of every thing in our universe. These pulsations funnel waves of consciousness inward from the border of the Universal UC toward creation, informing each new piece of material with its own unit of consciousness (UC) as it emerges from the universal portal of here and now.

Particles rush into our universe from the zero point field at the center, exploding outward, filling our universe from the middle. The outer fractal membrane presses inward to contain the energy exploding outward. Matter flows outward from the middle, repulsed by the energy streaming into the universe from the center, and coherence presses inward from the outer universal boundary. We experience the repulsive energy as “joy” and excitation, and the containing energy as “love” and security.

This cutaway view of the torus from the top shows ananda/joy exploding outward

and coherence/love pressing in.

This is the point in creation when the Universal UC is traditionally referred to by such names as “God the Creator,” “Shakti,” and the “Mother of 10,000 Things.”

Time passes and creation becomes more complex as subatomic particles reach out to one another according to the principles of organization conceived by the metaverse and set into motion by the Universal UC.

And particles joined to make atoms, atoms to make molecules, molecules to make single-celled organisms. Single-celled organisms diversified into the full panoply of life, and every one of these material building blocks came equipped with its own unit of consciousness (UC). Each unit of consciousness knew what particular role it needed to play in order to help the universe create and sustain itself, for every UC could decode and instantiate its own special piece of the metaversal ideal.

quanta UC

atomic UC

molecular UC

cellular UC

organism UC

societal UC

global UC





At each stage along the way from simple to complex, units of consciousness are increasingly sophisticated in their ability to regulate and manage their existence.

Sustaining Creation requires an uninterrupted stream of organization and intention funneling inward from the border that separates our space and time from the metaverse at large. Like pure potential pouring down the gravitational well of a great black hole, our possible futures become increasingly limited as they funnel toward the crucible of here and now at the heart of creation. Here and now, all potentials collapse as only one course of action is realized.

We generally refer to collapsed potential as “history.” The “future” is uncollapsed potential. There are an infinite number of potential futures that become increasingly constrained as they approach here and now. Here and now is the gateway of singular choice. The arrow of time flows downward through the middle of the torus, past here and now, and emerges into the past as a line of singular history. “Karma” is the consequence of historical choices made in the here and now.

Karma is the mechanism through which the consequences of behavior inform future potential. Karma is a force of influence that arises out of the decision-making history of every unit of consciousness in the universe. Each UC generates its own karma. We are all affected by one another’s karma. The more a unit of consciousness has in common with another UC, the more it is affected by the other’s karma. Our aggregate karma affects all of creation.

Tao te Ching -- Verse 53

The Tao Te Ching, or Book of the Way, is an ancient Chinese collection of 81 wisdom verses. In the "Simple Explanation” model, the Tao spoken of by Lao Tzu refers to the metaversal information and principles of organization that have informed our universe since the moment before creation; also known as the Universal Unit of Consciousness. Non-being refers to clearing your personal UC of earthly memes and karma. Non-action refers to allowing the original universal UC to direct your personal UC for the greater good. Here is the 53rd verse of the Tao Te Ching, which I have translated directly into Simple Explanation terminology from Jonathan Star's verbatim translation.

Staying centered near the vortex maintains alignment with the metaverse...

Verse 53

If those in charge possessed even the smallest bit of understanding,

they would follow nothing but the great metaversal way and dread straying from its main path.

The great metaversal path is very easy to travel, yet those in charge prefer taking side roads.

The seat of government is excessively well cared for, while the nation's fields are overgrown with weeds and the storehouses are all but empty.

Clothed in gorgeous garments, sporting the finest gadgets, gorging themselves with food and drink--bursting at the seams with more possessions than they could possibly use--this is recognized for what it is: the boasting of thieves.

This is the opposite of the metaversal path! Really!

______________________________________________

The Simple Explanation of verse 53 is that those in charge would make better decisions if they leaned not on their own self-serving understanding, but followed the principles of metaversal organization. This is expressed metaphorically as "staying centered" on the path. Using the torus as a visual model of staying centered looks like this:

The Simple Explanation's torus model showing the (white) line of metaversal information running through the zero-point center of here and now. This pole transmits the perfect choice for any given moment.

Not centering decisions within the metaversal plan leads to egoic decision-making, which is referred to as taking side paths. Self-centered decisions made by government officials, by definition, puts their interests above those in their care. This is because when we stray from the central path of wisdom, our choices are dictated by personal karma and memes rather than the greater good.

If the job of every unit of consciousness (UC) is to reach out to others with love, help, and information, that goes doubly for those sitting atop the hierarchical pile. The very reason for government is the care and feeding of those governed. For those in charge to ignore their "Heavenly Mandate" in favor of feathering their own nests is an abuse of power. Such abuse may prosper for a time but it cannot be maintained, as it goes against the metaversal plan.

Verse 53 says that the extravagent excesses indulged in by those in power comes at the expense of the greater populace. Lao Tzu likened such extravagence at the expense of others to "the boasting of thieves." He ends the verse with two exclamations to drive home the point! Really!

Readers of the Simple Explantion may realize by now that verse 53 not only refers to human society, but applies equally well to all other units of consciousness, be they sub-atomic particles, cells, or what-have-you. One of my favorite blog articles describing the hierarchical nature of the universe is "My Self, the Governor of Whoville." Once you see yourself as one who governs others, you will be closer to understanding how verse 53 applies to your life and your decision-making.

 

Is our Universal UC a gigantic autophagosome?

The cover of the March 26, 2011 edition of ScienceNews illustrates an autophagosome forming around some cellular debris. The second I laid eyes upon the cover, I was happy to see that this is very close to the mechanism I have been describing for the formation of our Universal Unit of Consciousness. Let's see how this might be a useful metaphor.

From the Wikipedia article, Autophagy,

A variety of autophagic processes exist, all having in common the degradation of intracellular components via the lysosome. The most well-known mechanism of autophagy involves the formation of a membrane around a targeted region of the cell, separating the contents from the rest of the cytoplasm. The resultant vesicle then fuses with a lysosome and subsequently degrades the contents.

According to the Science News article, Dining In, "In the first recognizable step of the process, a small, curved, double-membraned structure appears around the parts of the cell that are on the menu. That little bit of membrane grows to encase whatever the cell plans to swallow" (p.18).

Here's what the Simple Explanation says:

On this day that time began, consciousness wrapped itself around the expanding space of our universe, forming a border between us and infinity.

and again:

I'm suggesting that singular thought of limitless potential became a type of conceptual debris that needed sealing off from the undifferentiated metaverse. The torus shape suspends the singularity in the center zero-point field of our universe. Within our universe, time and space, matter and locality are held from the metaverse by this fractal membrane, the Universal UC.

Here's how I picture the process: imagine unfurling a large sheet, shaking it out above you, netting a big pouch of air, and quickly gathering up the corners in the middle. Voila--the Universal Unit of Consciousness, the prototypical toroidal shape, the essential fractal formula of creation.

The pouch of air inside the gathered sheet is our material universe, the sheet itself is the Universal UC, the fist holding the sheet corners at the middle is the ananda/joy/here/now point at the center of our universe, and the totality of the torus is the autophagosome container.

So, continuing with this metaphor, the debris that is this manifested universe will someday be simplified back to the building blocks of original consciousness and reabsorbed back into the undifferentiated metaverse.

*********************************

Changing gears, look at this beautiful illustration of little red autophagosomes lining up along the vortex of the toroidal shape that is cell mytosis. Isn't it gorgeous?

Fig. 1: Delivery of autophagosomes to lysosomes along microtubules.



A Simple Explanation of The Perennial Philosophy

A philosopher friend of mine recently commented on the Simple Explanation, "Excellent retelling of the Perennial Philosophy!"

I was unfamiliar with the expression "Perennial Philosophy," so I looked it up on Wikipedia. Here's their essential definition:

Perennial philosophy is the philosophical concept which states that each of the world’s religious traditions share a single truth. Perennial philosophy asserts that there is a single divine foundation of all religious knowledge, referred to as the universal truth. Each world religion, independent of its cultural or historical context, is simply a different interpretation of this knowledge...

Yes, my friend was right. The Simple Explanation is all about identifying the universal truth embedded underneath ages of confusing memetic overlays.

And what is the basic truth that all traditions share when you strip away their superfluous memes?

• There is a Divine Reality underpinning everything; without This, no thing and no one would exist. 
• Ground, Sat, Undiffentiated Unity, Brahman, Godhead, Pure Light of the Void, Pure Consciousness, Metaverse

• This Divine Reality may be directly perceived under certain conditions.
• through prayer, meditation, near-death experiences, mystic revelation, psychedelic drugs, religious ecstasy, inspired ritual, super-rational intuition
• Humans possess a dual nature: the little, egoic "me" of day-to-day living, and a true Self that reflects the Divine Reality.
• egoic "me" is selfish, competitive, single-minded, short-sighted, meme-bound
• transcending ego, Self reaches out to others with love, help, and information for the betterment of all
• People long to reunite with that divine Reality from whence they came.
• salvation, enlightenment, Self-realization, Buddhahood
• Unification is only possible through denial of the earthly self and identification with divine Reality.
• focus on the here and now; drop unwanted memes

          ****************************************

The late Aldous Huxley wrote an excellent book on the topic in 1944 called The Perennial Philosophy. I've only read the first three chapters so far, but they are already marked up with happy scribbles. What a smart man Huxley was! Everything he is saying fits in perfectly with the Simple Explanation, so if you would like a fuller explanation of the Perennial Philosophy, I'd recommend Huxley's book.

A Simple Explanation of the Tao Te Ching -- Verse 51

Prior to reading this post, please acquaint yourself with "Start Here: A Simple Explanation--Basic Principles" in the column on the right side of the screen. The Tao Te Ching, or Book of the Way, is an ancient Chinese collection of 81 wisdom verses. In the "Simple Explanation” model, the Tao spoken of by Lao Tzu refers to the metaversal information and principles of organization that have informed our universe since the moment before creation. Non-being refers to clearing your personal UC of earthly memes and karma. Non-action refers to allowing the original universal UC to direct your personal UC for the greater good. Here is the 51st verse of the Tao Te Ching, which I have translated directly into Simple Explanation terminology from an original verbatim translation by Jonathan Star.

Tao Te Ching, Verse 51

The Metaverse gives life to all things;

the Universal UC nourishes and protects them.

Every one of them materializes the form that best suits their nature, 

and challenging circumstances bring them to maturity and perfection.

Because of this, there is not a single UC that does not worship the Metaverse and treasure the Universal UC.

The Metaverse, honored.

The Universal UC, held dear. Truly, without it being demanded.
Yet constantly they come, each UC of its own accord.

This is why the Metaverse gives life to all things.

The Universal UC nourishes and protects them. 

Raises and ripens them,

nurtures them and educates them.

Shelters them. 

Matures them.

Sustains them and breaks them down.

Gives birth and yet does not claim possession of them.

Helps without expecting payment in return.

Fosters growth yet does not exercise authority.

Called secret, profound, obscure, mysterious, this Universal UC.

************************************

The translation above is based upon the cosmology explored in the Simple Explanation. Star's verbatim translation of "te" is "virtue" or "power." I have translated "te" as "principles of perfection" and "vitality," known as "chit" and "ananda" in Yogic philosophy. In identifying "te" as the Universal UC, I had the womb-like toroidal shape of the Universal UC in mind. Here we can see the undifferentiated unity of the metaverse separated out from the womb of creation where all things become manifest.

from the Simple Explanation article "Diagramming the Ineffable"

Notice that all things arise from this male/female creation principle, where the metaverse (male) supplies the spark of consciousness and organizational principles and the universal UC (female) contains, sustains, and nurtures the offspring.

Furthermore, Verse 51 makes clear that all things are "alive," not only the life forms we recognize. This is why the Simple Explanation treats every thing equally. Every thing is a fractal replication of the original Unit of Consciousness--the Universal UC. Therefore, every thing is an equally conscious being--a UC. The Simple Explanation suggests that what distinguishes one UC from another is its particular expression, which includes such variables as its material localization in time and space (i.e. point of view), its hierarchical organizational level, and its unique meme bundle and karmic record.

from the Simple Explanation article Nested Hierarchies

The depiction of the Divine given in Verse 51 is lovely. Far from being any kind of tyrant forcing mishaps and unfair destinies upon its unwilling subjects, this is a generational force that includes both male and female archetypes, providing every sort of nurturing care to its offspring. Despite its ability to command honor, respect, and devotion as the Great Creator and Sustainer, all UCs are free to honor their Creator spontaneously, in their own way, and free to construct their own destinies.

The Fractal Edge of Undifferentiated Consciousness

The Simple Explanation model suggests that the undifferentiated consciousness of the Metaverse is held apart from this created universe by means of a toroidal-shaped membrane "composed" of consciousness.

This conscious membrane (the Universal Unit of Consciousness) gives rise to countless fractal reiterations (Units of Consciousness, UCs) of itself, which in turn give rise to our material universe.

Which begs the question: How is it possible for an object (our Universe) to rest "inside" the formless Metaverse without affecting the undifferentiated nature of that originating place? How can space and non-dimensionality, time and timelessness, change and the changeless co-exist without touching the untouchable Metaverse? 

This paradox is easily solved by imagining that the membrane itself possesses a fractal surface, such as the Koch Curve. Through an infinite series of calculations, the fractal surface keeps itself contained and interiorized; keeping the undifferentiated unity of the Metaverse unsullied.

 

As you can see, through endless divisions, the surface and interior of the Koch snowflake remain contained to the figure, never reaching "outside."  The effect of this infinitely recursive fractal surface can be likened to that of an invisibility force field deployed around our universe, i..e, "What happens in our universe, stays in our universe."

Diagramming the Ineffable



Process Note:  The images above were laid out in Power Point off of the notebook page below:



Video Examples of Toroidal Flow

The Simple Explanation proposes that the fractal geometric equation upon which our material universe is patterned is toroidal in shape. Chapter 4, "One Simple Model," explains this toroidal flow model of the conscious universe. If you have not yet read the article "One Simple Model," this would be a good time.

This morning when I was running the blender, I noticed that the funnel formed by the blender's whirling blades is similar to the toroidal funnels created by the starburst of proto-energy at the heart of the universal torus pattern. For the metaphor to fully work, please imagine that the shape of the blender container is a torus and the whirling blades at the center is actually a zero-point field of infinite dimensions. Here's a one minute video of this morning's blender drink where I describe the blender's toroidal vortex.



After I posted this video to youtube, I saw that there were a number of other videos depicting toroids and toroidal flow. There must be many people like myself who are waking up to the toroids around  us. The following video of toroids I found on youtube is awesome! Way better examples of toroids than my blender funnel!

The Fractal Roots of Consciousness



As explained in the articles, "My Self, the Governor of Whoville" and "A Simple Fractal Model of the Conscious Universe," my Self's Unit of Consciousness (UC) is sitting atop a veritable fractal galaxy of hierarchically arranged Units of Consciousness, all working together to instantiate my body. While I may believe I am the only conscious soul inhabiting this body of mine, my physical body is actually home to all of these aggregated UCs, each with their own job to perform, each living their own lives and laying down their own karmic record. Within the confines of my skin, countless UCs of varying levels of complexity work together to keep my body alive and fully functional. At each descending level of complexity, from my governing Self UC down through the organ systems, organs, cells, molecules, atoms, and quanta, my body's UCs deal with increasingly simpler tasks even as the matter associated with them becomes smaller and more numerous. The simplest and most numerous level of materially instantiated consciousness is associated with the quantum foam that forms at the finest fractal edge between matter and energy.

As the roots of a plant send out finer and finer tendrils at each level of fractal branching, our hierarchically arranged aggregate UCs nest closer and closer to the Original Source Code--the Universal UC--at their simplest and most numerous levels. Whereas the concerns of the world often obscure my Self UC, the UC of a single sub-atomic particle or wave (anu), having a fairly limited view of creation and few choices regarding activity, is the least distracted by Ego and most attuned with its originating Source. At the deepest physical level of instantiation, the countless quanta that form the building blocks of our bodies are associated with countless undeluded UCs, all tapping their roots directly into the organizational source of our Universe ("Universal UC," "God," "Sat," "Original Source Code").

As I visualize the roots of Whoville, I visualize roots penetrating from my skin inward, finer and finer, to the depths of my material being. Within my body, all of my aggregated UCs drill fractally "backward" toward the zero-point field at our shared core. Whereas my Self UC may appear a long way off from God, especially if I conceive of God outside the Very Large, if I instead turn inward and "fall back," I am as near to God as the center point of Whoville's UCs. This is a new way to interpret the practices of "centering" and "grounding." When ancient teachings speak of God residing in the hearts of man, this Simple Explanation suggests the heart may be interpreted as the shared zero-point field at the shared center of our fractal Units of Consciousness.

Sagrada Familia -- Biomimetics and Architectural Symbolism

At the doctor's office the other day, I happened to see the December, 2010, National Geographic article on Barcelona's Sagrada Familia cathedral.  How this amazing structure, which has been under construction for a hundred years, passed me by until now is a mystery to me. The architect, Antoni Gaudi, designed this cathedral to uniquely reflect God's plan of natural structural design in contrast with the usual human approaches to architecture and engineering. The load-bearing columns, for example, replicate the twisting and branching structure of tree trunks rather than the normal design and arrangement of columns and arches typical of cathedrals. Gaudi also reflected God's plan in pure math forms, such as "Quadratic surfaces and conic curves: parabolas, hyperboloids, ruled surfaces."

The National Geographic article calls Gaudi's approach "biomimetic architecture."

Here's a quote from the National Geographic article:

"As idiosyncratic as Gaudí himself, it is a vision inspired by the architect's religious faith and love of nature. He understood that the natural world is rife with curved forms, not straight lines. And he noticed that natural construction tends to favor sinewy materials such as wood, muscle, and tendon. With these organic models in mind, Gaudí based his buildings on a simple premise: If nature is the work of God, and if architectural forms are derived from nature, then the best way to honor God is to design buildings based on his work. As the Barcelona scholar Joan Bassegoda Nonell notes, "Gaudí's famous phrase, 'originality is returning to the origin,' means that the origin of all things is nature, created by God." Gaudí's faith was his own. But his belief in the beautiful efficiency of natural engineering clearly anticipated the modern science of biomimetics."

Yes, toroidal forces appear is in this cathedral in many forms. Here's what Wikipedia says about the hyperboloids:

"Gaudí used hyperboloid structures in later designs of the Sagrada Família (more obviously after 1914), however there are a few places on the nativity façade—a design not equated with Gaudí's ruled-surface design, where the hyperboloid crops up. For example, all around the scene with the pelican there are numerous examples (including the basket held by one of the figures). There is a hyperboloid adding structural stability to the cypress tree (by connecting it to the bridge). And finally, the "bishop's mitre" spires are capped with hyperboloid structures.[9] In his later designs, ruled surfaces are prominent in the nave's vaults and windows and the surfaces of the Passion facade."

Here's an image of a hyperboloid

Do you see that this mathematical structure is also the central funnel of the torus? The hyperboloid shape can have a wide waist or a narrow waist.

 

Natural light is funneled through the cathedral's ceiling through numerous hyperboloidal skylights. Hyperboloid skylights allow more light to enter because light rays follow the same straight lines that create the circular cut-out. Take a look at the image of the hyperboloid above. Do you see how the grid lines that seem to swirl around are actually straight? A ray of light that enters along one of the grid lines at the top of the figure goes straight along wall of the hyperboloid through the middle to an apparently wider diameter than the size of the hole. A simple hole or tube only allows the light to go straight down the sides of the cut-out. 

The twisting of the columns also follows the hyperboloid which provides structural strength. A hyperboloid column distributes load more efficiently than a traditional straight column.

I personally love the skylights. To me, the light coming in through the funnel is a good visual metaphor for the light of God inspiring our path, or to put it another way, for the metaversal information pouring into our universe through our universal funnel.

 Watch for another article here soon discussing the symbology of the cathedral's spires...