Abstract
It is a well-known fact that numerous issues in many fields of human endeavor including, but not limited to, science and engineering, medicine, law enforcement and security, economics and finance, governance, psychology, philosophy, religion, and many other fields require the management of arbitrary dimensional data. However, systems permitting direct and efficient management of arbitrary dimensional data currently do not exist. In fact, contemporary systems such as graphical user interfaces for the management of data typically lack even the very concept of arbitrary dimensionality – failing to provide any practical way or means of managing arbitrary dimensional data. Here, we establish the foundational principles for a system permitting practical, direct and efficient management of arbitrary dimensional data. Furthermore, we demonstrate the effectiveness of our system by applying it to an experiment involving eight-dimensional (8D) medical and scientific data sets. Our system has immediate, far-reaching implications for numerous fields of human endeavor – enabling hitherto impossible solutions and applications and leading to deeper insights and improved understanding of numerous issues.
Highlights
SYNTHESIZING NEW INSTANCES OF ARBITRARY DIMENSIONAL DATANew instances of the user interface could be synthesized or created or computed by utilizing existing instances of the user interface
It is a well-known fact that numerous issues in many fields of human endeavor including, but not limited to, science and engineering, medicine, law enforcement and security, economics and finance, governance, psychology, philosophy, religion, and many other fields require the management of arbitrary dimensional data
Since a very large and growing subset of the data available to human society is amenable to processing or management on a computer or related systems which generally require interaction through a graphical user interface, we use the graphical user interface metaphor to elucidate the foundational principles of the system
Summary
New instances of the user interface could be synthesized or created or computed by utilizing existing instances of the user interface. Data within an instance could be represented as an image with elements comprising pixels or fractions of pixels (for sub-pixel precision) with the typical red, blue, green, alpha (RGBA) quad values for the associated red, green and blue color channels and alpha transparency channel and associated 3D coordinates x, y, z, and an optional time component that could be used in the case of video or time-varying image data In this case the foregoing equation for tri-linear interpolation could be interpreted as a pixel-wise operator permitting the synthesis of new pixels for new instances by utilizing the values of existing pixels for existing instances
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