Dear Stuti Kumar,

Any given measurement scale has a structure that depends directly on the number of causal factors. Thus a temperature measurement may a simple scalar reading; it could be further specified by adding of a two dimensional location on a well-defined surface. Locations in physical space (as within a volume of water) must clearly be specified using three-dimensionally specific scalar values. Thus, directions for a climbing route up a mountain might be described using the terms Left/Right, Up/Down and Forward/Backward, perhaps with modifiers specifying gradient and difficulty. Given this context, we may in principle model ‘ad intrusivness’ in a multi-dimensional cause and effect space. The model would have a new dimension for each added cause and may be optimized mathematically. Mentally, it necessary to avoid visualising entities such as hyper-dimensional space models. In effect we may simply select practical instances of effect, add and remove factors adlib, and attempt to predict them using least square optimization to refine the model.