Qualitative Geometry: The Intelligible Language of Meaning

The ruler & compass are 'analog tools' of the soul, connecting us in an unbroken chain to the past. They are some of the last remaining tools that require the 'slow brain' to engage with the 'fast universe'. They are tools of prescribing meaning to the universe, bringing order from chaos.

The Ruler: The tool of the Finite. It represents "Manifestation," "Duality," and "Matter." It connects two points in the shortest possible distance, representing the "Law" and "Logic." The ray of light follows essentially a ruled path through empty 3D Euclidean space, but can curve if the "paper" of four-dimensional spacetime is warped by mass.

The Compass: The tool of the Infinite. It represents the "Unmanifested," the "One," and the "Spirit." It has a fixed center (The Self/Source) and a moving periphery (The World). The star can be "circumscribed" only with a compass. The star's surface encompasses its fusion reaction which powers it and gravity warping four-dimensional spacetime gives it a hyper-spherical form. The circle is just the 2D shadow of the higher-dimensional mathematical reality.

Artificial Superintelligence (ASI) refers to an extrapolated future form of AGI (artificial general intelligence) that surpasses human intelligence across virtually all domains, including cognitive, creative, and problem-solving abilities. Unlike current narrow AI systems, which excel only in specific tasks, ASI would possess a level of intelligence far exceeding all of the brightest human minds put together simultaneously. ASI systems will outperform humans in every intellectual field, from scientific discovery to artistic creation and strategic decision-making, potentially enabling recursive algorithmic self-improvement and independent innovation beyond imagination.

"The inner governing archetype of a flower is the mystery of its species while the flowers of geometry are the 'timeless' forms of pure geometry. These can be provisionally expressed as indicating absolutes in geometrical drawings. The only tools required are a flat surface (a piece of flat supported paper), a pair of compasses with a scribing (or marking) point and a straight edge or ruler. (Both instruments can be replaced by rope, cord, or knotted thread, but this takes far more skill and practice and is usually used at a larger scale.) The language is in points, lines and surfaces or shapes. They are remarkably self-making or self-proving when drawn carefully, particularly when drawn by the human hand in an act of reverence and respect. The ancients described such an activity as 'participation.' The higher the goal the deeper the understanding."

"This wasn't just about appearances or relationships; it was an outward manifestation of an internal shift, an attempt to align my external self with the expanding horizons of my inner world. Studying at Berkeley, a campus large enough to contain multitudes, it became strikingly clear that the cultures of engineering and architecture occupied almost entirely separate psychological and even physical territories on campus. Engineering students, clustered in their labs and lecture halls on the north side of campus, often viewed the world through a lens of empirical data, logical systems, and quantifiable results. Architecture students, inhabiting the design studios and art history lecture rooms on the south side, tended to engage with reality through aesthetic sensibility, intuitive leaps, and the interpretation of cultural meaning. They were like two distinct species, speaking different languages, valuing different forms of knowledge, largely invisible to one another despite their physical proximity.

This observation led me to reflect on the notion, if somewhat simplistic for the sake of argument, of "left-brain" versus "right-brain" dominance. It seemed that most people, perhaps through early aptitude, educational tracking, or cultural reinforcement, tended to develop and prioritize one mode of thinking over the other. The left brain, with its penchant for analysis, sequence, language, and logic, felt like the natural home of the engineer. The right brain, with its capacity for holistic perception, spatial reasoning, intuition, and synthesis, seemed to be the domain of the artist and designer."

Clustered in labs and lecture halls, the "left-brain" mode prioritizes analysis, sequence, and language. It is the natural home of the builder who demands that the bridge must hold.

Quantitative Geometry: The geometry of the engineer. It asks: How big is it? How much does it weigh? Will it stand up? (The world of forces, dimensions and measurement).

In the "Standard Worldview," geometry is an inert but useful tool to anyone who wants to design and engineer stuff in the world.

The Circle: Is x²+y²=r² or "a plane figure contained by one line such that all the straight lines falling upon it from one point among those lying within the figure are equal to one another," according to Euclid.

At Berkeley, I saw these two distinct hominid species speaking different languages, largely invisible to one another despite their physical proximity. Most people are tracked into one territory or the other, weighted heavily on their one dominant side of the brain.

My work is in part my attempt to align the outer with the inner, the object with the subject, the society with the culture, the agency with the communion, the anima with the animus—to build the necessary bridge, the Corpus Callosum, between the North and South campus of the mind.

Inhabiting design studios and art history rooms, the "right-brain" mode prioritizes holistic perception and spatial reasoning. It is the domain of the visionary who asks why the bridge matters.

Qualitative Geometry: The geometry of the mystic and artist. It asks: What does it mean? How does it feel? What does it reveal about the nature of reality? (The world of meaning).

In our "Alternative Worldview," geometry is the living language of universal mind, which we all find intelligible, at least to some degree.

The Circle: Is the quality of Unity and Wholeness. It defines a boundary having an inside and and outside. What is me, and what is not me?

Qualitative Geometry is the art of reading the Code of the universe as if it were Poetry. It is the bridge that allows the Engineer to feel and the Artist to calculate. It is where the North and South campus of the mind finally meet in the center of the heart.

The sensitive students among us may start to feel like they almost remember something deep within the qualia of geometry. It happens when we see Truth in the geometry's perfection, palpably feel its Beauty, and bask in its undeniable Goodness. It is then that we are holding up a mirror to who we truly are, transcendental beings of pure consciousness. This is a BIG DEAL. It changes you. I can tell you, but you need to experience it yourself to really get it.

Ground your intuition in universal law. Learn the 'Code' that gives your vision unassailable structure.

Discover the poetry in your precision. Learn why the numbers you use every day are actually a gateway to meaning.

Absolutely. The "North and South Campus" is a metaphor for the two halves of your own mind. Most of us live "off-balance," favoring either cold logic or ungrounded intuition. Qualitative Geometry acts like the "Corpus Callosum" from the visible world of atoms to the invisible soul of your first-person experience—it is the practice of integrating your analytical mind with your spiritual heart. If you’ve ever felt that the world is more than just "empirical data" but struggled to find a logical way to explain that feeling, this work might be the bridge you’ve been looking for.

Most see geometry as a cold, 'North Campus' tool for measurement. But as I discovered at Berkeley, and later through my decades long study of the 'Invisible Domain,' geometry is actually the Corpus Callosum of the Soul. It is the bridge where the Left-Brain's precision meets the Right-Brain's meaning. That is because geometry, of all possible subjects, uniquely exists within the overarching Intelligible domain of Universal Mind. What else besides math, geometry, and music is universal?

Math is number in itself
Geometry is number in space
Music is number in time

The Qualitative Path is easy, just open your eyes and be guided to appreciate beauty. The Quantitative Path is complex, taking years to master the skills and the knowledge. The Mathematical Path is hard, you must prove it to be true with unassailable logic. All are the same geometry. What changes is you. Why not open up to a fuller universe that includes left, right, and center? They are all partial truth, partial beauty, partial bliss. When we integrate them we sense the ineffable exquistite perfection of the mathematical universe, finely-tuned to support each being's smile, laugh, their "Aha!" Moments.

Geometry is the only language that exists simultaneously in the engineering lab and the cathedral. This page invites you to stop choosing between 'how it works' and 'what it means' and start seeing the universe as a unified, intelligible masterpiece.