Fractal Information Theory (FIT)-Derived Geometric Musical Language (GML) for Brain-Inspired Hypercomputing

Abstract

We propose fractal information theory (FIT) to compute, and it uses a Fractal tape, wherein “every single cell of a Turing tape contains a Turing tape inside.” To use this tape, we introduce a geometric musical language (GML). This language has only one letter, a time cycle, a rhythm, a clock, or a unitary operator; on the circle perimeter, multiple singular bursts or “bings” (singularity represented as circles) are located. Time gap or “silence” between the “bings” is adjusted to hold the geometric parameters of structures such as square, triangle. Each time cycle is part of a phase space or a Bloch sphere; hence, information is now a “Bloch sphere with a clocking geometry.” Several such spheres self-assemble and expand like a balloon to store and process complex information; “bings” are singularity glue to add clocking Bloch spheres into it; this is the basic of fractal information theory (FIT). The conversion of five sensory signals into geometric shapes and rhythms like music and vice versa is called geometric musical language (GML). New information is integrated as guest into a single ever-expanding host Bloch sphere. The distinction between questions and answers disappears and replaced by “situation,” written as geometric shapes and always paired together in a time cycle, side by side or one inside another. Just like a human brain, FIT-GML hypercomputing does not require algorithm or programming, and it uses the fractal beating, i.e., geometric nesting inside a Hilbert space. FIT reduces to quantum information theory, QIT, if the clocking geometry in the Bloch sphere and virtual poles are removed and the singularity feature of a “bing” is eliminated, which makes it a classical state.