Bias-Independent Constructions from Biased Bisection and Adjacency Judgements

This paper discusses the possibility of using a biased bisection and its inverse operations intrinsically, to "correct for bias" and thereby to produce "corrected bisections" and related constructions, like concatenations or "sums" of sensory intervals. General results concerning the scope and limits of "corrected constructability" are derived, showing among other things that corrected sums can be constructed but corrected bisections cannot. Related issues include: (1) what can be determined by constructive means, e.g., that a given element correctly bisects an interval is shown to be determinable by these means, although it cannot be constructed by them; (2) a multidimensional generalization is considered, in which elements are represented by points in n-dimensional space and, paradoxically, it seems that corrected bisections can be produced in those spaces; (3) unsystematic comparisons to famous construction problems of geometry are made. Copyright 1997 Academic Press. Copyright 1997 Academic Press