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Symbolic Information In Computing Devices
1  ArborWay Labs


The extended abstract demonstrates how mathematical modeling reveals new information about physical symbols on the computer. A system of models based on Mark Burgin’s named set theory uncovers a uniform pattern of data relations hidden in the relational database. It is called the Aleph data relation. Its parent/child relationship is self-similar to a tree structure. The discovery of Aleph paves the way for transforming relational data into decision trees automatically. The system of models that led to this discovery also provides our first glimpse into a deeper, more balanced view of 0’s and 1’s on the computer. When modeling the migration of the Aleph in a decision tree over four different states, each graphic depiction is different because each one responds to different feature in the setting. However, when the model in each state focuses solely on the Aleph’s physical symbols and their parent/child relationship its composition remains intact over time and space. With this mathematical evidence, the author concludes that a deeper mathematical system holds the Aleph and its symbols together. With this in mind, the author proposes a theory on digital symbols based on these models. He believes that all digital symbols on the computer are composed of two meta-symbols: 1) physical-values and 2) constructed-types. The computer system employs these meta-symbols to manipulate strings of zeroes and ones, in a linguistic fashion, as types and tokens.