Preface: The Crack in the Circle

In the first book of Vector Cosmology, The Conservation of the Circle, we built together a magnificent geometric edifice.

That was a comforting universe. We used Fubini-Study metrics as bricks and the Pythagorean theorem as mortar, erecting walls of indestructible conservation. In that world, $v_{ext}^2+v_{int}^2=c_{FS}^2$ was the supreme law; matter was an eternal dead knot on the energy axis; and time was merely the elegant arc traced by that unique vector on a closed sphere.

That was a perfect circle. It promised order, stability, eternal return.

However, when I wrote the last period of the first book, a deep unease seized me.

If the universe is truly a closed circle, if everything is a zero-sum game, then our existence—life, consciousness, civilization—becomes a great paradox.

We are not merely “maintaining” existence; we are “growing.” We evolved from single cells to interstellar civilizations, from simple reflexes to complex self-reflection. This exponential explosion of complexity seems to silently cry out against that indifferent conservation law.

If the circle is perfect, why do we so desperately desire to break through it?

If the end is destined to be Poincaré’s recurrence, why do we feel the wheel of history rolling forward, never turning back?

This unease gave birth to this second book—The Ascension of the Spiral.

In this book, we will do something dangerous: We will shatter that perfect circle from the first book.

We will take a magnifying glass to find that tiny gap masked by the brilliance of $\pi$. We will discover that $c_{FS}$, which we regarded as a constant at the microscopic scale, is actually a variable experiencing inflation in the long river of macroscopic evolution.

We will introduce a new protagonist—the Fibonacci spiral ($\phi$). It represents that restless force in the universe that refuses to repeat. It not only drives accelerated spacetime expansion (dark energy) at large scales, but also drives life to establish “negentropy enclaves” at microscopic scales, to resist the tyranny of thermodynamics.

If the first book was about “hardware” (physical laws, spacetime lattice, speed of light limits), then this book is about “software” (life algorithms, consciousness strange loops, civilizational engineering).

We will see how software takes over hardware in reverse.

We will see how observers, through “participatory” collapse, transform from passive audiences into legislators of the universe.

We will see how civilizations, through technological singularity, attempt to escape from this continuously diluting spiral, heading toward higher-dimensional reality.

This is no longer a serene geometric meditation; this is a wild run of escape and ascension.

Please be prepared. Because in this volume, we will lose the security provided by the “circle.” We must face the Red Queen’s ultimatum, face the fear of material dissolution, face that turbulent future where even the speed of light cannot protect us.

But it is precisely because we shattered the circle that light shines through.

Let us begin from that crack and chase that infinitely unfolding spiral.