Real Numbers Are Not the Hidden Variables of Anything

Gisin and Del Santo have argued, in a series of influential papers (2019–2023), that real numbers are the “hidden variables of classical mechanics,” on the grounds that a typical real number contains an infinite amount of information that a finite volume of space cannot store. We show that this argument rests on a fundamental confusion between a physical quantity and the number that results from its numerization. The infinite sequence of decimals of a real number is not a property of the world but the structural product of the measurement procedure: the iterated application of a standard to an independent magnitude. The generic incommensurability of any two magnitudes of the same kind suffices to generate this infinite sequence. We identify and name three nested confusions: the word–thing confusion (the word “magnitude” taken for the real quantity), the quantity–number confusion (the real quantity taken for its numerical value), and their product, the numerization confusion, through which the real disappears from both sides at once. We show that these confusions symmetrically vitiate both classical determinism and Gisin’s informational indeterminism, and sketch the consequences for the determinism/indeterminism debate.