This presentation is about new directions of study and discovery in both Mathematics and Science. Over the last several centuries, science has discovered objects in the world along a continuum of scale. In one direction, we have found planets and stars, galaxies and galaxy clusters. In the other direction we have found cells and proteins, atoms and neutrinos. In order to locate and model this world, we use the 3 traditional directions of length, width and height. However inherent in all our measurements is the scale of the objects we are measuring — a continuum we do not directly see with our eyes. A key reason we do not include this direction as part of our scientific models is that we do not have the appropriate mathematical tools to take measurements along this continuum. New mathematical tools may require a numeric representational system with more power than our traditional decimal or positional based numerals. Such a more powerful system may provide a single value for complex numbers able to measure across scale and adds to its structure the reversing operations of integration and differentiation. The ability to calculate integration and differentiation results would be a powerful mechanism for applied and for pure mathematics. The author presents some opening remarks on what is anticipated to be a much larger discussion, looking at a model of reality where objects at all levels of scale can be located and considers directions for generating more powerful mathematical tools than we have today.