The Rao Theorems
“All knowledge is, in final analysis, history.
All sciences are, in the abstract, mathematics.
All judgements are, in their rationale, statistics.”— C. R. Rao
Background
The following three theorems are attributed to
Calyampudi Radhakrishna Rao (C. R. Rao),
one of the most influential statisticians of the modern era.
They appear on the front matter of his work Statistics and Truth and articulate a concise structural view of how knowledge, science, and judgement operate.
The Rao Theorems are not derived within the EMIS Framework. They are treated as an established epistemic synthesis.
EMIS focuses not on their proof, but on explaining why such patterns recur across disciplines.
Theorem I · Knowledge as History
All knowledge is, in final analysis, history.
Knowledge exists as accumulated records of past observations, experiences, and interpretations.
Even the most abstract theories are grounded in historical processes of discovery, validation, and revision.
Theorem II · Science as Mathematics
All sciences are, in the abstract, mathematics.
Scientific understanding relies on abstraction.
When stripped of context and implementation, scientific theories reduce to mathematical structures describing relations, constraints, and transformations.
Theorem III · Judgement as Statistics
All judgements are, in their rationale, statistics.
Judgement under uncertainty is inherently statistical.
Whether explicit or implicit, rational decisions depend on probabilistic reasoning, estimation, and inference from incomplete information.
Interpretation within EMIS Framework
Within the EMIS Framework, these statements are treated as structural regularities of human knowledge and judgement, rather than empirical laws governing physical reality.
Within the EMIS Framework, the Rao Theorems are best understood as:
Meta-theorems about how knowledge, science, and judgement are structured.
They do not describe how the world moves,
but how we perceive, abstract, and evaluate the world.
- History compresses experience.
- Mathematics compresses structure.
- Statistics compresses uncertainty.
Together, they explain why efficient systems of knowledge favor abstraction, formalization, and probabilistic reasoning.