The Theory of Data: An Introduction

Abstract

The Theory of Data describes analytical quantities independently of their storage and execution. It asks which analytical points exist, what a quantity means at those points, which transformations preserve its meaning, and what information supports a later calculation. This introduction develops that account through revenue, averages, distinct counts, and closing values. It explains the central reference, a measure family at an anchor, then separates the formation of a quantity from its continuation. It presents sufficient state as a relationship among ordinary measure families, introduces the governed FIRST/LAST construction, and distinguishes a correct answer from retained information adequate for another use. The governing reference is the published Theory of Data v7.1. The examples explain its laws; they do not add new ones or assert implementation coverage. This edition succeeds Version 2.2 and aligns the Introduction with the published Theory of Data, Version 7.1. It preserves the sixteen-section teaching progression and develops family formation, sufficient-state families, governed FIRST/LAST, evidence adequacy, and materialized reuse through concrete examples.