When Representation Is Mistaken for Analytical Meaning

Database and analytics systems are very good at representing data and computing with it. The harder problem is deciding what an analytical result is about, what makes it valid, and which transformations keep its meaning. The Theory of Data answers those questions with its own terms, and each resembles something familiar: a population looks like a fact table, an anchor like a grain, a measure like a metric, a value state like a stored value, and a measure law like a function. This paper takes the familiar terms one at a time, says what each is mistaken for, and shows a small constructed case where the mistake produces a wrong number: an order counted once per order line, one key on two rows doubling a customer's orders, distinct counts summed across months, NULL read as zero, one AVG giving two averages, a false key repeating pipeline in every quarter, and lifetime spend summed down the days of a result table. A final case shows how a benchmark's hand-written reference queries can inherit the same mistakes. In each case the system computed exactly what it was told; it failed where representation was taken for meaning. Representation and computation can realize analytical meaning. They do not define it. The paper uses the terms of The Theory of Data v9.1.1 and the setting of The Three Worlds of Analytical Data v3.0.1.