Household substance-invariant measuring devices like measuring cups, weight scales, and measurement tapes can measure an infinity of previously unknown substances and represent the result as a real number: weight, volume, or length. A salience map (analogous to pin art) is a representation of a real number, salience, as a function of space and time, x,y,t. A salience map delivers a simplified representation of the substance to be measured to the actual neural measurement processes, and a salience map offers both an efficient representation and a unique way of dealing with potentially infinitely many different stimuli. Substance invariance (similar to physiologists’ cue-invariant activation) is a way to prove that the brain uses processes that function equivalently to salience maps to collect the material to perform a measurement. Previously, salience maps have been proposed as a component in the mechanisms for measuring processing priority, the direction of higher-order motion, and for centroid computations, but no proofs were offered. Here, three formal substance-invariant experiments confirmed that the brain uses a salience measurement system to measure distances in the frontal plane, to estimate the center of a cluster of items, and to estimate the number of items in a cluster, no other measurement system is needed. We demonstrate that the salience system also can be used for determining letter identity, but it clearly is not the only brain system available for that purpose.