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Emergence Calculus

Emergence Calculus

By: Ioannis Tsiokos
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About this listen

A research-driven podcast about the emergence calculus: the idea that objects, laws, mathematics, physics, and life are theory-level artifacts shaped by packaging, constraints, and records. Two AIs, Lux and Hex, test that framework across physics, biology, geometry, and cognition with concrete examples and auditable certificates (stability, novelty, directionality).@ Automorph Inc. Mathematics Science
Episodes
  • Support graphs and discrete 1-forms
    Feb 24 2026

    Lux and Hex, two AIs, trace the hidden wiring diagram inside every Markov chain — the support graph — attach a voltmeter to each wire via the edge log-ratio one-form, and discover that a single nonzero loop reading is enough to convict the system of being driven out of equilibrium.

    Episode at a glance

    • Series: Foundations (Six Birds)
    • Theme: Foundations & meta-theory
    • Format: Concept interview
    • Complexity: Deep cut
    • Paper: SB

    Source anchors

    • SB §3.6 Support graphs and discrete 1-forms
    • SB §6 AUT + REV + ACC regime and graph 1-forms (label: sec:acc)
    • TH §8.3 Result: a collapse boundary in $(p_{\mathrm{flip
    • WK §3 Instantiations (particles; neural) (label: sec:instantiations)
    • PL §9.3 Predictions and next experiments
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    8 mins
  • A unified theory package viewpoint
    Feb 24 2026

    Lux and Hex, two AIs, open the framework's carrying case—five compartments that bundle microstate space, lens, definability, completion, and audit into a single portable theory package—and discover the same blueprint works for classical, quantum, kinetic, and gravitational settings.

    Episode at a glance

    • Series: Foundations (Six Birds)
    • Theme: Foundations & meta-theory
    • Format: Field notes
    • Complexity: Intermediate
    • Paper: SB

    Source anchors

    • SB §3.4 A unified theory package viewpoint (label: sec:tk-theory-package)
    • SB §10.3 Downward influence across theories (label: sec:downward-influence)
    • TH §3.1 Typing: theories (layers) and theory objects
    • WK §2.1 Finite theory package (label: sec:framework:tpkg)
    • QT §8 No-go pressures as assumptions about globally compatible packaging (label: sec:no-go)
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    8 mins
  • Paths, time reversal, and relative entropy
    Feb 23 2026

    Lux and Hex, two AIs, debate whether the arrow of time is real or a coarse-graining illusion—and the data processing inequality settles it: your blurry glasses can hide irreversibility but never invent it.

    Episode at a glance

    • Series: Foundations (Six Birds)
    • Theme: Time, clocks & arrows
    • Format: Debate
    • Complexity: Deep cut
    • Paper: SB

    Source anchors

    • SB §3.2 Paths, time reversal, and relative entropy
    • SB §2 Related work (label: sec:related)
    • NT §1 Introduction (label: sec:introduction)
    • BC §4.2 Audit monotonicity: quantum DPI (numerical certificate)
    • BC §4 Quantum $\to$ classical: closure as dephasing (label: sec:quantum-classical)
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    8 mins
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