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

Why Publish a 56 Percent Failure Rate?

Fourteen of twenty-five registered predictions failed. The failures turned out to be the most useful part.

Method · 8 min
03

It Matters When You Defected

Two histories with identical scores and certain, different futures. The difference is not in the game's books.

Society · 7 min
04

A Hundred Instruments, One Blind Spot

Agreement is not objectivity. What counts is whether some instrument tells the right worlds apart.

Foundations · 7 min

III. Papers

All papers
  1. 01 Reflexive SBT and Anti-LocalizationThree auditable capacities that rule out hidden spikes. →
  2. 02 To Lay a Stone with Six BirdsWhat a system needs to carry all six birds by itself. →
  3. 03 Persistence of SPT-LegalityWhen spreading out at every scale survives the dynamics. →
  4. 04 Building What a Proof NeedsA method for building the helper world a proof needs. →
  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.