Distortion of Visual Space as Inappropriate Constancy Scaling

The expected frequency-of-scores set for a (n,1') maze is therefore: [VT(a)(r,n)/(~)} (J. = 0, 1,2 ___ n_ These and other statistics concerning the distribution of scores may be used to define parameters for the maze which may be related to subjective difficulty_ In this notation m/j equals the number of pathways between dot i and dot j with zero score (i, j = 0, 1, 2 ... r, f) : and if m,j > 0, then we may say that dot j is directly accessible from dot i. Developing this concept we may use a binary notation in the form of matrix M' = (m'if) (i, j = 0, 1, 2 , .. r, f) where m'if = 1 if mlj > 0 (that is, if j is directly accessible from i) and = 0 otherwise. Matrices Veal', T(t)', T("', T(3)I may also be derived corresponding to the unprimed matrices given here. The basic difference between the two sets of matrices is that in the first set the number of different pathways with score ex between dots i and j is considered, whereas in the second series the number of different sets of ex dots lying on pathways between dots i and j is the underlying concept. Thus, for example, v o / m)' gives the number of different solution sets of dots. Further, the dots (not including 0 andf) may be divided into n groups corresponding to the n horizontal maze rows, and the vector (dp) may be defined, where d p = number of dots on the pth horizontal maze row (p = 1, 2 The matrix M' may now be partitioned into sub-matrices RaP where a, 13 refer to maze rows; here 'maze rows' are taken to include a zero row and an f row and so GC, 13 = 0, 1, 2 ... n, j. Ra{J is a d a x dp matrix which gives direct accessibility relationships between dots on the ex th row and the 13 th row. Again, RaP = 0 if ex ~ 13. Since one theory describing maze problem-solving activity postulates that individuals differ in the size of the perceptual unit which they use, it seems relevant to illustrate one way in which the present approach could be used to analyse this aspect of the problem. To do this we have defined as a tJ. alty maze-linked set of dots. A …