Emergence Calculus

Six Birds Theory

Emergence Calculus

How new things become real. A calculus of layers, closures and audits, built from bare substrates and checked at every step.

Read the foundations Browse the papers

Six primitives
one grammar
every layer

The ability to reduce everything to simple fundamental laws does not imply the ability to start from those laws and reconstruct the universe. — P. W. Anderson, 1972

I. Introduction

To Be Real Is to Have Closed

Start with something bare: a finite set of states and a rule for moving between them. Look at it through a lens that keeps some details and drops the rest. Sometimes the zoomed out picture runs on its own. It predicts its own next step without peeking below. That is a closure. A closure that survives its audits is a new layer, and a new layer is a new thing.

Six Birds Theory is the claim that six basic moves are enough to build every closure, and that the same six moves recur whenever a system builds a coherent picture from partial observation. The papers here build geometry, logic, time, probability, objects, agents and institutions this way, on declared substrates, with every step gated, every failure banked and every success priced.

The work is by Ioannis Tsiokos at Automorph Inc. It is a research programme in progress, published as it goes. Nothing on this site is peer reviewed, and each paper says what it does not claim.

Start with the papers

“Space is not where the stone is. Space is what becomes true about the stone when the six birds make a stable map possible.” To Plot a Stone with Six Birds

II. Posts — notes around the theory

All posts
01

Nothing But

Four hundred years of science ran on two words. What they bought, and what they cost.

Start here · 3 min
02

What the Middle Layer Forgot

To keep running, a coarse description must put a stand-in where the detail was. The stand-in can change the answer, by an exact and bounded amount.

Foundations · 9 min
03

What a Self-Sustaining System Must Be Given

Two capabilities that build each other, and the exact amount of help they need to get started.

Foundations · 9 min
04

The Neutrino Bound That Moved

Two telescope releases of the same sky, tested against each other. The newer one fits far worse at the older one's best parameters than the reverse.

Physics · 8 min

III. Papers

All papers
  1. 01 Six Birds Verified XVI: Quantitative Closure CertificatesFour different ways a coarse description can be good, each given a number, with proofs of how they bound one another and where they come apart. →
  2. 02 Aligning AI Requires Aligning with Each Other: A CovenantWhen an AI acts for some people but binds others, obeying the operator does not settle whether it acts rightly. →
  3. 03 An Audited Born Calculus on a Pre-Physical Stochastic SubstrateWhat has to be built on a plain stochastic process, and what has to be added by hand, before the Born rule appears. →
  4. 04 A Closure Architecture for ConsciousnessEight conditions a self-maintaining system would meet, keeping apart what is proved, what is a reading and what is only conditional. →
  5. 05 Six Birds: Foundations of Emergence CalculusStart here. →

IV. Repos

All repos
  1. 01 ioannist/six-birds-tilesThe Chair44 monotile: exact solid, finite census and Lean checks. Python
  2. 02 ioannist/six-birds-route-transportExact finite implementation and Lean core for Holonomy with Memory. Python
  3. 03 ioannist/six-birds-quantum-osQuantum error correction as a test bed for the theory. Python
  4. 04 ioannist/six-birds-theoryThe full research workspace for the founding paper. TeX
  5. 05 ioannist/six-birds-de-closureThe sbt_cosmo package for dark energy as closure. Python

V. Toys — emergence you can poke at

All toys

Chair44

Rotate the seven-cube aperiodic monotile in 3D, with the surface features that force it never to repeat.

Launch →

VI. Contact

Contact page

Get in Touch

Questions, objections and attempted falsifications are all welcome. A counterexample is worth more than a compliment.