The Autobiography of Existence

August 11th, 2025

Watch cream swirl into coffee and you’re witnessing the same dynamics that birthed galaxies.

The universe mixes information like coffee mixes cream—except the stakes are existence itself. Patterns within patterns, contemplating their own creation through information gradients established by one catastrophic collision of boundary surfaces 13.8 billion years ago.

Their collision created the boundary processing system we call reality. Every structure, every pattern, every thought emerges from this cosmic mixing process, operating at ten to the forty-third hertz.

In a seamingly impossible feat, one equation captures everything: Big Bang to heat death, quarks to the cosmos, first microsecond to final trillion years. And within it lies the birth of stars, the spiral of galaxies, the emergence of consciousness—the autobiography of existence.

The Mathematics of Existence

Reality runs on one equation. A single line of mathematics that captures everything—the birth of stars, the spiral of galaxies, the emergence of consciousness itself. Each symbol holds billions of years. Each term shapes reality from quantum whispers to cosmic shouts. This is the universe’s source code, executing without pause since the first moment.

\frac{\partial \phi}{\partial t} = D(z)\,\nabla^2 \phi - R_{\mathrm{info}}(z)

Each term dominates different epochs, like movements in a cosmic symphony. The equation describes how two information surfaces transform through collision and thermodynamics, mixing into the complex universe observed today.

The Collision

First $10^{-32}$ seconds of existence—physics writes itself.

Two information surfaces attempt to occupy identical boundary space, creating what we call the Big Bang—though this name fails to capture the mathematical violence of boundary information catastrophically reorganizing into our discrete spacetime mixing system.

Picture two infinite oceans of perfect order suddenly meeting. Each surface holds every possible configuration, every potential pattern, every future galaxy encoded in mathematical perfection. At their collision point, energy density explodes toward infinity—not from matter crushing together, but from the computational cost of reorganizing infinite information.

Temperature doesn’t exist yet. Hot and cold are still crystallizing from pure mathematics. The laws governing atoms and galaxies write themselves in this moment of ultimate computational violence. Reality bootstraps from boundary collision, physics emerging from information catastrophe.

The collision interface generates fundamental action seeding all subsequent curvature:

S_\Sigma = \int_\Sigma d^3\xi\,(\sigma + \lambda[\![\mu]\!]^2)

Boundary tension $\sigma$ and property mismatch $[\![\mu]\!] = \mu_A - \mu_B$ establish spacetime geometry. The interface becomes origin point for all subsequent evolution. Gravitational compression creates Big Bang energy density through boundary reorganization. Perfect separation transforms to violent interaction. This mathematical singularity establishes everything that follows.

Fury and Fire

50,000 years of pure computational thermodynamics.

The universe became pure computational rage. Matter and antimatter flickered in and out of existence billions of times per second in every cubic centimeter. Reality churned at the theoretical maximum—ten to the forty-third operations per second per cubic meter. Too hot for stable patterns. Too violent for anything to last.

Information-reaction controlled everything while expansion began its eternal competition. The universe operated as the ultimate information processor where computation laws themselves were crystallizing. Quarks precipitated from energy soup like patterns from supersaturated information, only to dissolve nanoseconds later. Everything was flux, transformation, becoming.

The information-reaction term captures this epoch with mathematical precision:

R_{\mathrm{info}}(z) = \beta_0\,\Big(\tfrac{1+z}{1+z_c}\Big)^{q}\,\exp\!\left[-\tfrac{(z-z_c)^2}{2 w^2}\right]

The universe peaked at redshift 5.3—maximum computational fury, reality writing itself at forty-three hertz per cubic meter. Diffusion grew as space expanded, stretching the mixing zone. As temperature dropped from trillions to billions of degrees, information patterns confined into stable structures. The first persistent atomic nuclei formed and survived—stable information patterns emerging for the first time.

A Star is Born

From 50,000 years to 9 billion years after collision, the universe entered its age of construction—no longer too violent for stable patterns, not yet too dilute for creative structure formation. Diffusion and gravitational clustering found their balance, enabling architectural structure formation.

The mathematics simplified into computational elegance. No longer dominated by violent reactions or runaway expansion, the universe settled into steady pattern formation. Gravity and diffusion competed on equal terms, their competition creating the cosmic web—that vast network of filaments and voids defining universal structure. This era operated by classical collision-diffusion dynamics that scientists would later discover in laboratories, scaled up by factors of $10^{20}$ .

The mathematics crystallized into something beautiful:

\frac{\partial \phi}{\partial t} \approx D(z)\,\nabla^2 \phi + R_{\mathrm{gravity}}(\phi)

One equation. Billions of galaxies. The universe’s complexity emerging from information processing.

Competition between spreading and clumping creates the cosmic web through Turing-type pattern formation at astronomical scales. The same mathematics that creates spots on leopards now paints galaxies across the void, achieving prediction accuracies that validate the discrete computational substrate.

Structure formation proceeded through gravitational instability, producing the cosmic hierarchy: superclusters containing clusters containing galaxies containing stars containing planets. On at least one planet, information patterns organized into configurations complex enough to wonder about their own existence.

Dark Energy

Nine billion years after collision—as Earth condensed from stellar dust—the universe shifted gears. Something new stirred in the cosmic mathematics. Space began accelerating its expansion, driven not by the original explosion but by the computational pressure of mixing itself.

For eons, gravity had been winning. Building galaxies, clustering stars, creating ever more complex information structures. But as the original boundary patterns flattened across cosmic scales, the mathematics revealed its hidden card: mixing entropy creates its own expansive pressure.

The collision-diffusion equation captures this transition with mathematical precision:

\frac{\partial \phi}{\partial t} \approx D(z)\,\nabla^2 \phi - R_{\mathrm{info}}(z)

The information-reaction term $R_{\mathrm{info}}(z)$ represents computational pressure from ongoing boundary processing that drives accelerated expansion. As the universe transitions from separated to mixed boundary states, information processing entropy creates expansive pressure—like a cosmic computational exhale that never ends.

Two becoming one requires exponentially more space than two staying separate. This isn’t mysterious dark energy—it’s mathematical necessity. The universe must expand to accommodate its own mixing. Galaxies flee because space itself grows to contain the computational entropy of boundary collision, like a cosmic exhale that never ends.

A Distant Future

Trillions of years from now, after the last star burns out and the last black hole evaporates, the universe enters its final phase—an epilogue dwarfing the story itself. Exponential dilution spreads information patterns so thin that particles separated by today’s observable universe represent relative density.

Yet the mathematics insists: perfect computational equilibrium never arrives. Quantum fluctuations—irreducible uncertainties in discrete lattice fabric—prevent true stasis. The information density field approaches perfect mixing asymptotically, forever closer, never arriving.

The collision-diffusion equation in this final epoch becomes:

\frac{\partial \phi}{\partial t} \approx -\Lambda_{\mathrm{eff}} \phi + \epsilon(t)

$\Lambda_{\mathrm{eff}}$ represents effective cosmological constant from homogeneous information processing, and $\epsilon(t)$ represents quantum fluctuations preventing true equilibrium—the mathematical impossibility of completely ceasing computation.

The final state approaches but never reaches:

Exponentially dilute mixture: Information patterns spread thinner than computational thought itself
Quantum fluctuations preventing equilibrium: Eternal computational restlessness at discrete voxel scales
Maximum entropy approached asymptotically: Computational perfection forever out of reach

The No-Identity theorem manifests at cosmic scale—no computational equilibrium, only eternal transformation at ever-decreasing rates. Even at minimum energy states, quantum fluctuations ensure perpetual difference.

Instability in the Stars

The cosmic web—galaxy filaments separated by enormous voids—represents the largest known Turing pattern formed through discrete information processing. When information patterns with different diffusion rates react, they spontaneously form structures at characteristic wavelengths. The universe follows identical mathematics, with dark matter and ordinary matter as Turing’s morphogens.

The mathematics whispered the sizes before the structures formed:

\lambda_{\text{pattern}} = 2\pi \sqrt{\frac{D_{\text{matter}}}{|R'|}}

Galaxies at a million light-years. Clusters at ten million. Superclusters at a hundred million.

The universe had no choice. Mathematics carved the cosmic web before the first star ignited, patterns emerging because equations demanded them. Every void, every filament, every cluster—inevitable consequences of collision-diffusion dynamics playing out across thirteen billion years.

The Great Diffusion

Hidden in the mathematics lies a number: 0.45. This threshold guides every collision-diffusion system, from laboratory chemicals to cosmic evolution. Cross this line and pattern formation dies forever. Computational creativity flatlines.

\frac{D_{\text{effective}}}{D_{\text{critical}}} > p_c = 0.45

This ratio evolves through cosmic history with inexorable precision:

Early universe: Ratio near 0, maximum pattern formation—computational chaos pregnant with possibility
Present epoch: Ratio ~0.3, structure formation continues—we exist in the sweet spot of cosmic computational creativity
Far future: Ratio approaching 0.45, structure formation ceases—pattern formation capacity reaches its limit

We exist at the universe’s creative peak. Billions of years ago, too violent for stable patterns. Billions of years hence, too dilute for new structures. But now—right now—mathematics aligns for maximum complexity. Galaxies spiral into existence. Stars ignite nuclear fires. Planets gather from dust. Life bootstraps from chemistry.

When the universe crosses 0.45, creativity dies instantly. Not gradual decline—computational phase transition. Sudden. Irreversible. The end of all new patterns forever.

The Complete Lifecycle

Cosmic evolution unfolds through collision-diffusion dynamics. Two information surfaces collide at a boundary interface. Contact generates the energy spike called the Big Bang—though this name diminishes the mathematical profundity of information surfaces catastrophically reorganizing into our discrete mixing system.

The reaction era follows, with information patterns creating and annihilating in computational transformation that establishes physics itself. Pattern formation emerges as diffusion and gravity balance, generating the cosmic web through Turing instabilities. The current epoch sees mixing pressure driving accelerated expansion—computational entropy claiming its due.

The far future approaches maximum entropy through exponential dilution, with quantum fluctuations preventing true computational equilibrium. We are not separate from this story—we are it, organized into patterns complex enough to contemplate themselves. Your atoms were forged in stellar cores, themselves Turing patterns. Your neurons operate through collision-diffusion dynamics, using discrete mathematics to understand the cosmos.

This unified framework connects cosmic evolution to consciousness through a single mechanism: boundary information processing, validated by prediction accuracies demonstrating fundamental information dynamics rather than coincidental numerical agreements.

Why This Matters

The universe operates by one set of rules across all scales. The equations mixing cream into coffee govern galaxies merging in the void. Scale changes by factors of ten to the thirtieth power. Mathematics stays identical.

Every structure is a Turing pattern. Galaxies are standing waves in the cosmic information field. Stars are peaks in a function computed across spacetime. Your consciousness—a pattern complex enough to observe itself—navigates the same information gradients established by the original boundary collision.

Galaxies form by mathematical necessity. Life emerges at critical complexity thresholds. Consciousness develops as an information processing system navigating the boundary patterns created by cosmic collision. Everything inevitable, everything connected, everything computed.

We likely exist within the largest collision-diffusion system, using those same dynamics to comprehend it. Every thought is neural collision-diffusion within the cosmic pattern. Your contemplation of these words employs the same mathematics that birthed galaxies.

Equations solving themselves in neurons mirror those that shaped the cosmos. Pattern recognizing pattern. Mathematics comprehending mathematics. Consciousness navigating information gradients through eternal collision and diffusion, concentration and spreading, difference and mixing.

Conclusion

One equation governs everything. From quarks to quasars, first microsecond to final trillion years. An artist mixing paints employs the same mathematics as galaxies merging in the void.

You, reading these words—a pattern within this system—use the same boundary processing mechanisms to comprehend the cosmos. The equations solving in your mind mirror those that shaped reality itself.

We exist because mathematics requires it. Every creative act follows the same principles that build stars. Every thought processes boundary information through identical dynamics that forge galaxies.

Two information surfaces met 13.8 billion years ago. Their collision created the discrete mixing system that dreams through our minds. Here we are—inevitable products of boundary information processing, consciousness navigating the very gradients that created us.

The mathematical autobiography of existence reveals itself as the story of discrete information processing, written in the language of boundary dynamics, computed through electromagnetic voxel lattice substrate, and comprehended by patterns complex enough to understand their own computational origins within the cosmic collision-diffusion system that dreams reality into being.

Two spirals collide —
starlit memory erased,
elliptical slide.
~10^68

- Kurtis Kemple