StaTesc — statistics inside the number
Real life carries partial truth, ambiguous choices, and irrelevant-but-known information. StaTesc gives digits for each — so probability is not bolted onto arithmetic, it lives inside every numeral.
Why statistics is foundational, not downstream
Classical arithmetic assumes complete information: every digit is fully known. StaTesc — the digit algebra defined in LaeStaDesc — generalises that assumption. Each digit is read as a triple φ(d) = (s, t, u) of spatial truth, temporal truth, and uncertainty. Ordinary numbers, Boolean values and Kolmogorov probabilities are recovered as special cases when u = 0.
The StaTesc digit set 𝒟
Ten symbols cover the interior life of numbers. Three are used most often: U for spatial uncertainty, ∪ for temporal uncertainty, and ∅ for structural absence.
- Spatial uncertaintyU
- Either A or O — a 50/50 spatial value carried inside the digit itself.
- Temporal uncertainty∪
- Either I or E — a 50/50 temporal value; time-band ambiguity as a numeral.
- Bound uncertainty∩
- Companion to ∪ — restricts the temporal ambiguity to a resolvable band.
- Upward reversibleV
- Uncertainty that propagates up the positional band; useful for unknown future effects.
- Downward reversibleW
- Mirror of V — known but currently irrelevant details that resolve downward.
- Structural absence∅
- A digit that is not a digit — placeholder for missing data, optional fields, gaps.
Three operations, three axioms
AND behaves as multiplication, OR as addition, NOT as unary minus — the same shapes classical arithmetic uses, but uncertainty propagates through them coherently. The whole system rests on three axioms:
- Associativity. Regroup freely; results agree.
- Band-precedence. Temporal meaning dominates spatial meaning when they meet.
- Uncertainty monotonicity. AND increases uncertainty, OR decreases it.
Lifting these digit-wise operations to numbers gives an arithmetic in which "known", "unknown" and "structurally absent" travel side by side. See section 4 of the LaeStaDesc README for the full multi-band operator table and its correspondence with Logecs connectives (MULT, ADD, NOR, XOR, NET).
Statistics as an interface layer
StaTesc is the interface between Real Logecs (numbers and truth) and Natural Logecs (measurements and populations). Every reading of a physical instrument already lives on this layer; StaTesc simply lets it be written down without a separate probability apparatus.
Because the digits are octave-symmetric — every band rescales by two — statistical numbers stay recognisable when zoomed in or out, the same self-similarity that makes tones repeat across octaves:
Continue with
- LaeStaDesc — full README (popular, applied and formal introductions in one file).
- Real Logecs — the number and truth substrate StaTesc extends.
- Spiritual Reasoning Logecs — where uncertainty meets experience, improvisation and Dukkha.