Grand Biological Universe: Genome space geometry unravels looking for a single metric is likely to be futile in evolution

Understanding the differences between genomic sequences of different lives is crucial for biological classification and phylogeny. Here, we downloaded all the reliable sequences of the seven kingdoms and determined the dimensions of the genome space embedded in the Euclidean space, along with the corresponding Natural Metrics. The concept of the Grand Biological Universe is further proposed. In the grand universe, the convex hulls formed by the universes of seven kingdoms are mutually disjoint, and the convex hulls formed by different biological groups within each kingdom are mutually disjoint. This study provides a novel geometric perspective for studying molecular biology and also offers an accurate way for large-scale sequence comparison in a real-time manner. Most importantly, this study shows that, due to the space-time distortion in the biological genome space similar to Einstein’s theory, it is futile to look for a single metric to measure different biological universes, as previous studies have done.