Modeling imageless thought: The relative judgment theory of numerical comparisons

The mental process of comparing numbers is shown to follow the principles of Relative Judgment Theory. Martingale predictions of the theory are confirmed in an extensive study of numerical comparisons using the Method of Symmetric Differences. The theory is then used as a tool to reveal the Psychonumeric Function relating psychological difference to numerical difference. This function transforms a difference between numbers into a sextal valued (0, 1, 2, 3, 4, 5) number with zero as a unit psychonumeric value. The Psychonumeric Function combined with the theory's prediction of response times gives a close account of the numerical comparison Chronometric Function.