ABSTRACT
The results to which the foregoing chapter has just led us—the initial difficulty in 'composing' displacements then a successful conclusion in the form of a grouping of formal operations— lead naturally on, by way of a counter check, to the study of relative movements. The movements used in Chapter Four are movements in series and the composition of these simply consists of adding them together as if two changes of location made up only one single one (this is moreover, the essential characteristic of 'groups': the two operations combine into but one). On the contrary, relative movements are simultaneous, e.g. the movement of a passenger on a boat in motion. Their composition then consists of considering them as if they were in succession and adding them up in the same way as the previous ones, e.g. the boat, has moved ahead the distance X and the traveller (on the boat) the distance Y hence the total journey (in relation to the shore) is (X plus Y) if they are going in the same direction or (X minus Y) if their directions are opposite. But it may be seen at once that intuitively this relativity of movement appears to be more difficult to grasp than the composition of movement in succession, since attention must be brought to bear on the two movements simultaneously. Operationally, on the contrary, the composition of the movements is the same whether they are in succession or simultaneous. It is therefore of interest for us to compare a problem of relative movements with the earlier problems in such a way as to make clearer the respective roles of intuition and operations.
