Authors: Donald G. Palmer
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 what we are measuring — a continuum we do not directly see with our eyes. The author presents the hypothesis that we need to include this continuum in a complete model of nature and our world. A key reason we do not understand this direction as part of our world is that we do not know how to measure along this continuum because we lack the mathematical tools to do so. The author presents the mathematical conjecture that the appropriate tools require a numeric representational system with more power than our traditional decimal or positional based numerals. Such a system could provide a single value for complex numbers and has built into it more operations than addition/subtraction, multiplication/division, and exponentiation/logarithms (from whence the new system gets its additional power). The author anticipates this to be the beginning of a much larger discussion, looking at a perspective of reality where objects at all levels of scale exist and interact together and considers some directions for defining more powerful mathematical tools than we have today.
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