Real Logecs
The face of Laegna that handles number, logic, and math realms — including thermodynamics as a math object. Spiritual models with claims in logic and math are verified or reproduced here, in symbolic form.
What lives inside Real Logecs
Real Logecs is Laegna's mathematical core. It treats logic, numbers and math realms as one connected system rather than separate courses, and exposes them through a small, coherent notation.
- Two-bit truth⟨t,f⟩
- Every proposition carries two bits — one for its truth, one for its falsehood — so contradiction, unknown and partial truth are first-class values, not exceptions.
- Infinity notations∞ · 0̸
- A calibrated family of infinities and zeroes (see LaeArve, LaeSpiEssentialTheorems / InfinityAndZero) so infinite quantities can be compared, added and integrated inside proofs, not only in limits.
- Statistical numbersμ ± σ
- Probability enters as a fundamental number, not a theory bolted on top: projecting 3-D space into any 3-D coordinate system requires an arbitrary origin, so context-dependence is part of the number system.
- Unknowns / openness digits?
- Digits that symbolize openness allow statistical objects to be written as ordinary numerals — incomplete information stays inside the arithmetic instead of leaking into ad-hoc comments.
- ThermodynamicsS · dQ/T
- Zero-states, energy flows and entropy are treated as native math objects. Any machine that maximizes energy efficiency automatically speaks the same paradigm — a shared scale for real and computed systems.
Instruments of Real Laegna
Three interactive instruments illustrate Real Logecs end-to-end and are also linked from spireason.neocities.org:
- Sheep — counting, the primitive from which every number system descends.
- Handheld calculus — Laegna calculus as a tactile object, derivatives and integrals as gestures.
- Exponometer — given two numbers, computes acceleration and exponent; in the right standard units the two values are numerically equal.
From Boolean to two-bit and beyond
FuzzyLogecs is the canonical text for Real Logecs' truth model. Classical Boolean logic is a degenerate case where the truth bit and the falsehood bit are always opposites; in Fuzzy Logecs they run independently, so (1,1) is contradiction, (0,0) is unknown, and (1,0) and (0,1) recover the classical values.
Combined with statistical numbers, this gives an inference calculus where "how much we know" and "how much of it is true" travel through formulas together — the way real reasoning already does.
Where real Laegna is developed
Deeper mathematical treatments live in LaeMath (see MathFuncs) for functions, and LaeArve as the development centre — its README opens with two chapters linking Laegna Infinities to a single reference point of alternatives.
For classical-science relations and the collected essential theorems, see LaeSpiEssentialTheorems, where Laegna and SpiReason are kept in clearly separate folders.