Visualizing a Fourth Dimension: Hypercubic Resistor Networks

A booming field in physics research today is the search for extra dimensions. This is something that has been thought about and discussed in both the scientific and non-scientific world for a long time. Many physicists are currently attempting to answer the question: "is our world really four dimensional?" The purpose of this research, however, is not to answer that question. The purpose of this work is to help reveal four-dimensional artifacts in our perceived three-dimensional world in order to help a student, even a non-physicist, to understand and visualize how the extra spatial dimensionality, if present, might reveal itself in measurements. To that end, models of non-trivial four-dimensional objects have been constructed that have consequences large enough to be easily measured and understood in an intuitive fashion. In building and analyzing data from two, three, and four-dimensional model systems with non-trivial interactions, large and conceptually transparent consequences of extra spatial dimensions have been discovered.