The Barrier to Human Understanding of MARS

Repaginated 5 October 2026: content unchanged; pages 22-52 of Vol. 1 No. 2 (formerly 21-51), following the version 1.1.0 corrections to the Foundations entries 000 and 007–010. Version 1.1 (October 2026): clarifications for practitioners — active hinges by knot position, the reflected hinge as a shrinking discount, the double knot, interactions and the sales grid, and the alternatives to MARS.A supplement to the first movement of this issue's Foundations entries. The four statistical entries, 007 to 010, reason about the rate a regression assigns to a feature; the Journal's own modelling uses multivariate adaptive regression splines (MARS), which report one rate per range rather than one per feature. This supplement shows, on one worked model of living area in a coastal market, how the terms a MARS program prints become a rate table, the value contribution of a quantity of the feature, and the adjustment from a comparable to a subject, defined as the amount added to the comparable's contribution to make it equal to the subject's. It states the one rule hand-built tables get wrong: a reflected hinge h(t - x) has slope -1 where it is active, so a coefficient of -600 on h(1200 - gla) is a rate of +600 a foot below 1,200 square feet, not -600. It shows why the single rate an ordinary regression would need for a given pair is the chord between the two contributions, an average that changes with the pair. A Prolog program, printed in full and published with its 62 tests, reads the coefficient table of the R package earth, prints the rate table, the values at the knots, the adjustment range by range and the OLS-equivalent rate, and checks that the ranges sum to the adjustment. The tests pass under Trealla, SWI-Prolog and Scryer Prolog.