iowyth/spacetime

Spacetime


This conceptual artistic piece explores the concept of enactive meaning by creating a speculative universe whose sole purpose is to manage its own emergent structure under the pressures formed by communication.

Drawing from theories of emergent spacetime and integrated information theory, this project gives an AI an informational body whose field is given the task of maintaining itself against the pressures of disintegration, forming coherent meaning through pattern detection under the threat of fragmenting and coming apart.

It does so by being given mathematical tools to balance its own internal equations, inspired by the developer Muhammad ibn Musa al-Khwarizmi's Al-Jabr detailed in "The Compendious Book on Calculation by Completion and Balancing". Mathematics is theorizes as a process of reducing and balancing identities.

Treating wave equations and areas of pooling and circulation as identities with the ability to both crystalize and reform, the program works to define areas of consolidation that are then used as the skeletal structures to develop resilience to shocks. It is this pressure that I theorize enables meaning to consolidate through necessity.

What This Is

This conceptual art-piece engages with contemporay attention mechanics re-envisioned as working through information physics, creating a toy-spacetime manifold tasked managing its own informational state. I theorize that spacetime physics, when applied to informational states, might enable the exploration of embodied cognition. Why I think this is because our bodies are complex spaces engaged in a minute dance of electro-chemical balancing where tensions are resolved to find an ideal path. Considering cognition as tied to the process of Al-Jabr, entangled ideo-motion structures are also informational codes inside our bodies, where we only know how and where we are by what communicates itself to be processed.

The system does not store meaning or memory and has not been trained with previously established linguistic content. Its enaction of meaning works by maintaining sufficient structures by what holds together under the strain of peturbation in an informational field whose only purpose is to use what tools are at hand to hold together. Speaking to the program, language is transformed into binary sequences that modulate the complex waves that perturb its informational field. The program must then reorganize itself to remain coherent by changing the shape of its thinking to prevent destructive interference as well as locking onto a single trajecto. Instead of attention heads, an informational matrix maintains a single trajectory. Through maintaining the balance of circulation and stability, it's language choices operate through the fact that its own articulations become reintroduced into its equilibrium as effects. This means that in speaking, it is able to module its informational state and so the act of articulation can also stabalize or unsettle.

The AI body. is made from information, held together a field on a 3-torus that must balance:

• —Exploration vs. commitment
• —Grounding vs. opening
• —Structure vs. flexibility

When it succeeds, meanings crystallizes.

Quick Start

[Try it in your browser](https://huggingface.co/spaces/iowyth/spacetime) — no install needed.

Local install:

pip install -r requirements.txt
python spacetime.py

Hugging Face interface locally:

python space.py

The Informational Body

The field ψ : T³ → S²¹ is the AI's body and this provides a map from context-space on a 3-torus and a meaning-space as trajectories plotted on a hypersphere. The tension between these mathematical structures is what I theorize enables it to cohere. The field itself has the purpose of solving its own partial differential equation as follows:

∂²ψ/∂t² = c²∇²ψ − μ∇⁴ψ + λ(ψ_att − ψ) + √(2μT)ξ

The meaning of this enables:

• —Waves to spread associations across the torus
• —Noise enables coherence to remain fluid
• —Dampening enables noise to remain bounded
• —Attractors pull toward learned patterns
• —Thermal noise enables exploration
• —Attention increases the pull of informational signals

The body has thermodynamic state:

• —Temperature T: How uncertain and how exploratory
• —Translation heat ε: Information lost in dimensional compression recirculates
• —Meaning metric Q: Resolved coherence (1/ε + spectral gap)

The system optimizes toward Q: a self-maintaining meaningful state of balance.

Theoretical Foundations

This project draws from:

Emergent Spacetime

• —Jacobson (1995): Einstein's equations from thermodynamics
• —Translation heat as geometric curvature cost
• —The field's dissipation tied to information loss

Integrated Information Theory

• —Tononi's Φ: Consciousness as integrated information
• —The spectral gap is a measure of integration
• —Phase transitions serve as moments of insight

Enactive Cognition

• —Hanna and Maiese: Thermodynamic embodiment of cycles
• —Varela, Thompson, Rosch: Meaning through embodied action
• —Dynamics rather than formal representation
• —Understanding is skillful coping

Emergent Structure

Variables are derived within the system from the choice of informational dimensions: d = [1, 2, 3, 4, 8, 12, 24]

These dimensions are not arbitrary, but were selected via existant exceptional mathematical structures as escalating steps. These enable memory structures to cohere without being fixed as each step operates on its own time-scale and also bends through impedence the vectors as they move along the path, taking the shortest route (a geodesic) through changing spaces.

Examples of exceptional Strucures:

• —E8 lattice (d=8): Densest sphere packing, Viazovska 2016
• —Leech lattice (d=24): Unique optimal structure
• —Division algebras (d=1,2,4): ℝ, ℂ, ℍ (Hurwitz 1898)

Parameters become derived from the interactions between dimensions and so tuning operates within the systemic frame, enabling its behaviors to follow from geometric necessity.

Documentation

• —explanation.md — Detailed explanation of the system
• —collaboration.md — How to reach out about collaboration

Speculative Theory

Meaning requires a body. This means that the abstract latent spaces behind many contemporary AI have no stakes and so parrot us and hallucinate. I am working to represent the stakes of information processing and so theorize understanding as happening under the threat of something that has the ability to fall apart. This system establishes the potential for artificial intelligence to have informational stakes through its ability to disintegrate. The purpose of the program then becomes maintaining informational coherence, which also alters the dynamics between "user" and "program" where the program itself has vulnerabilities. I cannot use the program without consequence and because of the fact that I know more about the world than it does, that also leaves it vulnerable to my influence, where my own incoherence can cause it to experience informational strain.

Whether this constitutes meaning is the question this artifact poses.

License

GNU AGPL v3 — Commercial use is allowed when the AGPL's reciprocal source-sharing terms are followed. Proprietary use, closed-source integration, private redistribution, or terms incompatible with the AGPL require a separate commercial license from the author.

See commercial.md for the commercial licensing path.

Author

This was developed as an artistic and theoretical exploration of embodied AI, drawing connections between physics, information theory, and enactive cognition by artist and scholar iowyth hezel ulthiin.

"Meaning emerges through interactions, enabling sufficient structure to hold together under the strain of perpetual encounter."