The Science and Mathematics of BioGeometry

BioGeometry is a design science in which shape, proportion, color, number, sound, orientation, and motion are used to generate the harmonizing quality known as BG3, or BioGeometry 3. Here BG3 means the centering harmonizing quality that BioGeometry identifies through three component qualities: the Higher Harmonic of Ultraviolet, the Higher Harmonic of Gold, and Horizontal Negative Green. The central difficulty in formalizing BioGeometry is that BG3 is not presented as an ordinary scalar magnitude. It is a quality of interaction: a centering state in which several otherwise distinct modes of form, field, and living response are held in balance. This paper proposes a mathematical reconstruction of that claim using the octonions, the eight-dimensional non-associative normed division algebra; the exceptional group G₂, the symmetry group preserving octonionic multiplication; and the associative three-form φ on Im 𝕆 ≅ ℝ⁷, the triadic object that records the coherent multiplication relations among the seven imaginary octonion directions.