The Laegna & SpiReason ecosystem

• spireason.neocities.org

  Counting (#sheep), Laegna calculus (#handheldcal) and infinity (#infinity) interactive materials.

  Hub
• laegna.notaku.site

  Introductions to Laegna and SpiReason; in-depth infinity essay at the anchor #1ac75bfc1154809b8037da3fbfaaf000.

  Notes
• github.com/tambetvali

  The parent organisation for Laegna and SpiReason repositories.

  Repos

• SimplyAboutInfinities

  Primary text on Laegna infinities.

  Book
• Second Attempt

  The main chapter within SimplyAboutInfinities.

  Chapter
• Axiomatic

  Parallel / appendix to Second Attempt.

  Appendix
• FuzzyLogecs

  Canonical text for Laegna's two-bit truth model — its README is the main text.

  Book
• LaeStaDesc — StaTesc

  Statistical digit system: uncertainty, partial knowledge, reversible states and mixed temporal–spatial meaning as first-class numerals.

  Book
• SpiritualReasoningLogecs

  How Logecs opens to experience, improvisation and the ideal ↔ real contrast — the mathematical substrate for spiritual and ethical reasoning.

  Book

• LaeMath

  Alternative source of Laegna math for mathematicians.

  Math
• MathFuncs (LaeMath)

  Main functions page inside LaeMath.

  Reference
• LaeArve

  Development centre; README opens with two chapters linking Laegna Infinities to a single reference point of alternatives.

  Dev centre
• laGEOsis

  Laegna Lane Geometry.

  Geometry
• LaeLane

  loglinexp → linlin → lin growth functions, hashing and comparing scales; base-3 octaves and beyond.

  Growth

• LaeSpiEssentialTheorems

  For classical-science relations; collected (non-exhaustive) essential theorems. Laegna and SpiReason are kept in clearly separate folders.

  Bridge
• InfinityAndZero theorems

  Reconstructs a complete axiomatic source alongside laegna.notaku.site — the two cross-validate.

  Set

• exponometer.app

  Main applet: from two numbers, acceleration and exponent — numerically equal in the right standard units.

  Applet
• Sheep (counting)

  The primitive counting instrument.

  Applet
• Handheld calculus

  Tactile Laegna calculus.

  Applet
• Infinity

  Laegna infinities — discussed in SpiReason.

  Applet

Notation alone does not make a field incompatible with developing Laegna math — quite the opposite. Every concept Laegna opens up also opens up an existing shelf of combinatorics, geometry, logic or physics that a working reader will want to consult. The list below is a starting map: authors and works whose treatments are domain-complete enough to understand what is done around each idea, even before any Laegna translation exists.

Combinatorics of internal/external angles, axiomatic method, incidence structures — Laegna's geometry lives on top of this scaffolding.

• David Hilbert

  Grundlagen der Geometrie (1899)

  Rigorous axiom sets for lines, planes and angles — much of Laegna's geometric combinatorics has direct correspondents here.

• Euclid

  Elements

  Original common notions and postulates; the reference every non-Euclidean or extended geometry, Laegna included, must eventually meet.

• Felix Klein

  Erlangen Program (1872)

  Geometries classified by their invariance groups — the reading frame for LaeLane's octave-scale invariants.

• Emil Artin

  Geometric Algebra (1957)

  Coordinate-free treatment of reflection, useful for reasoning about wave-reflection symmetry in Laegna numbers.

Two-bit truth and infinity notations extend, not replace, this tradition. Reading the classics keeps translations honest.

• George Boole

  The Laws of Thought (1854)

  The degenerate case (t = ¬f) that Fuzzy Logecs generalises.

• Gottlob Frege

  Begriffsschrift (1879)

  First real predicate calculus — the surface Laegna's notation must remain compatible with.

• Bertrand Russell & A. N. Whitehead

  Principia Mathematica

  Full derivation chain for classical mathematics from logic; useful comparison for Laegna's own primitives.

• Kurt Gödel

  On Formally Undecidable Propositions (1931)

  Where closed logic hits its ceiling — exactly the boundary Logecs' openness is designed for.

• Georg Cantor

  Contributions to the Founding of the Theory of Transfinite Numbers

  Original infinity hierarchy; SimplyAboutInfinities cross-validates against it.

• Ernst Zermelo & Abraham Fraenkel

  ZFC axioms

  Baseline set theory the Laegna Infinity axiomatic runs parallel to.

• Lotfi Zadeh

  Fuzzy Sets (1965)

  Prior art for graded truth — a helpful contrast to Laegna's independent two bits.

• Jan Łukasiewicz

  On Three-Valued Logic (1920)

  Historic non-Boolean logic; useful ancestor for multi-valued reasoning.

For understanding what StaTesc reframes and what Laegna number preserves.

• Richard Dedekind

  Was sind und was sollen die Zahlen? (1888)

  Foundational construction of the reals — the object statistical digits extend.

• Giuseppe Peano

  Arithmetices Principia (1889)

  Axiomatic natural numbers; the base from which counting instruments like Sheep descend.

• Andrey Kolmogorov

  Foundations of the Theory of Probability (1933)

  Axiomatic probability that StaTesc turns from bolt-on to native.

• Thomas Bayes / Pierre-Simon Laplace

  Essay towards solving a Problem in the Doctrine of Chances / Théorie analytique des probabilités

  The classical grammar of updating belief — same problem StaTesc rewrites with digit-level uncertainty.

• Abraham Robinson

  Non-standard Analysis (1966)

  Consistent calculus with infinitesimals; kin to Laegna's calibrated infinities.

Why Laegna number is built to survive doubling and halving on every axis at once.

• Pythagoras (via Nicomachus, Ptolemy)

  Harmonics / Pythagorean tuning

  Original doctrine that doubling a length reproduces the same tone — the octave symmetry Laegna number preserves.

• Hermann von Helmholtz

  On the Sensations of Tone (1863)

  Physical basis of pitch, timbre and consonance — the sensory side of octave self-similarity.

• Joseph Fourier

  Théorie analytique de la chaleur (1822)

  Decomposition into harmonics; the mathematical basis for reasoning about signals across octaves.

• James Clerk Maxwell

  A Treatise on Electricity and Magnetism (1873)

  Waves as first-class physical objects that carry the same octave scaling as sound.

• Benoit Mandelbrot

  The Fractal Geometry of Nature (1982)

  Formal language for self-similar, scale-invariant structures — a modern cousin of the octave principle.

The runtime Laegna Logex sits next to, and the information theory its statistical digits refine.

• Alan Turing

  On Computable Numbers (1936)

  The reference model of mechanical computation Logex is measured against.

• Alonzo Church

  The Calculi of Lambda-Conversion (1941)

  Function-first computation; useful contrast for Logex's connective-first style.

• Claude Shannon

  A Mathematical Theory of Communication (1948)

  Information as a quantitative object — the layer StaTesc extends with structural absence and reversible bands.

• John von Neumann

  First Draft of a Report on the EDVAC (1945)

  Stored-program architecture — the target energy-efficient Logex machines must eventually beat on shared thermodynamic terms.

Zero-states, flows, entropy — where Natural Logecs and classical physics already agree in substance.

• Sadi Carnot

  Réflexions sur la puissance motrice du feu (1824)

  Original efficiency limits — the shared paradigm any max-efficiency machine already speaks.

• Rudolf Clausius / Ludwig Boltzmann

  Founding papers of statistical mechanics

  Entropy as counting; kin to StaTesc's digit-level uncertainty.

• Erwin Schrödinger

  What is Life? (1944)

  The bridge from thermodynamics to living systems Laegna's Natural Logecs walks across.

The classical shelves behind Logecs of Mind — read to see what Logecs formalises and what it deliberately keeps open.

• William James

  The Principles of Psychology (1890)

  The stream of experience as an object worth measuring — Logecs' opening move.

• Charles Sanders Peirce

  Collected Papers

  Triadic sign relations and abductive reasoning; deep prior art for openness-in-inference.

• Edmund Husserl

  Ideas I (1913)

  Phenomenology as a discipline of intentional structure — vocabulary Logecs of Mind can borrow cleanly.

• Buddhaghosa

  Visuddhimagga

  Systematic treatment of Dukkha; the classical reference behind Laegna's Dukkha and Treth notation.