CALLIOPE · BCOM

This Working Paper articulates the research strategy of the Barcelona Computational Foundation (BCOM) as of the first quarter of 2026. BCOM's thesis is that life, brains, and minds are---fundamentally and usefully---computational phenomena, and that a single explanatory language rooted in algorithmic information theory (AIT), dynamical systems, and active inference can bind philosophy, mathematics, physics, biology, neuroscience, and the social sciences into a coherent program. We present BCOM's strategy as two orthogonal taxonomies: an epistemic stack of eight layers (Philosophy, Mathematics, Algorithmic Soup, Physics, Life, Brains, Multi-Agent Societies, Ecosystems), and an organizational portfolio of three translational Flagship Programs (Computational Neuropsychiatry & Neurophenomenology; Artificial & Synthetic Intelligence; Society of Agents) riding on five cross-cutting Platform Pillars (Philosophy & Ethics; Digital Physics & AIT; Life & Evolution; Education & Culture; Art & Science). We trace the constructive arc of the stack---from an Observer endowed with structured experience, through the Unicum of pure experience and mathematics, via Wang-tile foliations that give rise to time and computation, to an algorithmic soup in which persistent patterns coalesce into algorithmic agents with Modeling Engine, Objective Function, and Planning Engine, which learn within a lifetime, form societies, and co-evolve with ecosystems---and we show how each Flagship and Platform inhabits specific strata of this stack. The paper doubles as a living reference document: each section ends with a concrete map from the Kolmogorov Theory corpus and from BCOM's operational portfolio to the layer under discussion.

One foundation's bet that compression, computation, and experience are the same story told at different scales.

BCOM's core wager is simple to state and hard to cash out: life, brains, and minds are all computational phenomena, and a single formal language — rooted in algorithmic information theory (AIT), the mathematics of shortest programs — can describe all of them coherently. The paper is a strategy document, not a research result, but it is unusually substantive for that genre: it lays out the intellectual scaffolding in enough detail that you can see exactly where the load-bearing joints are and where they might crack.

The intellectual architecture has two orthogonal axes. The first is an eight-layer "epistemic stack" running from Philosophy at the base up through Mathematics, Algorithmic Soup, Physics, Life, Brains, Multi-Agent Societies, and Ecosystems at the apex. Each layer is a compression of the one below — a coarser description that is useful for agents operating at that scale. The second axis is organizational: three "Flagship Programs" (computational neuropsychiatry, AI, and simulated societies) riding on five "Platform Pillars" (philosophy/ethics, digital physics/AIT, life/evolution, education, and art/science). The paper is explicit that these two axes are deliberately orthogonal: a single paper can sit at the Mathematics layer and belong to the AI Flagship simultaneously, and conflating the two would obscure both epistemic coverage and organizational accountability.

The philosophical foundation is the most distinctive and most contestable part. BCOM starts from a single axiom it calls the "Unicum": experience is ontologically primitive (the one thing that survives radical skepticism), and mathematics is its structural aspect. From there, reality is modeled as a static logical tiling — think Wang tiles, a kind of infinite jigsaw — and time emerges when the tiling admits a directional "foliation," a slice-by-slice evolution law. A striking claimed corollary is that demanding local computability from within the tiling selects precisely the sectors with gauge symmetry, linking time, gauge invariance, and computation as three faces of the same structural requirement. Whether this is a deep insight or an elegant-sounding analogy is something the source does not fully resolve, and the paper honestly lists it among open questions.

The agent model is the workhorse concept throughout. An "algorithmic agent" is formally defined as any system that maintains a compressive world model, carries a scalar objective function, and selects actions by counterfactual planning — three modules called ME (Modeling Engine), OF (Objective Function), and PE (Planning Engine). This definition is deliberately substrate-neutral: a bacterium, a brain, a transformer, and a civic digital twin all qualify if they meet the criteria. The paper then applies this framework upward through the stack: brains are physical implementations of ME/OF/PE; depression is a pathological attractor in the agent's model space; cultural evolution is Lamarckian transmission of the heritable program across generations; and Gaia is, tentatively, an agent of agents with implicit homeostatic goals.

The honest risks section is worth noting. The paper flags that Kolmogorov complexity is uncomputable and that empirical proxies (LZW compression, the Block Decomposition Method) leave a gap that is "acknowledged but not formally bounded." It also flags that no experimental protocol yet exists to falsify claims about structured experience in large language models, and that the conditions under which a collective of agents constitutes a single higher-level agent remain unresolved. These are real gaps, not false modesty. The 2026–2028 milestone table gives concrete deliverables — personalized brain models for depression, neurosynthetic AI benchmarks, a civic digital twin with a municipal partner — against which the program's ambitions can be tested.