With these visual methods it is possible to approach the investigation of massive data sets in a systematic and rational manner as compared to the chance discoveries so often associated with the serendipitous use of scientific visualization software. All of these visual methods trade off the more accurate and traditional quantitative techniques for a more qualitative but comparative visual techniques. These visual methods indeed parallel how we first imagine our functions and mimic our first impressions of possible relationships. This "combinatory play" of images does indeed seem to be the essential feature in productive thought and such an approach is shown here to work well when visualizing the gradient of a scalar function by the cognitive visual data compression method and the extraction of algebraic expressions embedded in distributed numbers. Both methods require the exploitation of new graphical features such as rotating voxel volume translucency and the more simple colored moving ("gradients") in three dimensional space. These examples perhaps are first serious attempt of extending our mechanism of thought where "psychical entities" that represent physical quantities can be also shared with others as images.