ABSTRACT
So far we have been able to observe that even if direct linear (normally rectilinear) order is given intuitively, the various relations of order (inverse linear order and cyclic order in both directions) are completely formed only when 'grouped' into an operational system which might be called a grouping of 'placements'. Turning now to movement or 'displacement', which viewed qualitatively is only a change of place or order, we have already been able to establish that the path traversed, or the interval between starting and finishing points, remains undifferentiated from the order itself, so long as this last remains intuitive: on the one hand, the distances covered are at first gauged solely by the finishing points, and on the other hand the integral and indivisible nature of movement as a change of position directed towards a goal or end-object prevents their measurement. It is only when order reaches the level of concrete operations (7 to 8 years) that paths traversed are conceived as intervals or distances capable of subdivision, and open to operational qualitative or metrical evaluation. Thus it is now apposite to study the actual operation of change of position, which, if the foregoing analyses are accurate, may be conceived either in terms of operations of order, as a change of position or dis-placement, or else in terms of the intervals contained between the sequence of positions, as a summation of distances.
