The Geometry of Biology

The Geometric Approach

Much of modern biology is organized around measurements. We collect observations, arrange them into tables, and search for variables that differ between conditions. This approach has been enormously successful, but it can sometimes obscure a deeper question: what if biological systems are better understood not as collections of measurements, but as states occupying positions within a high-dimensional space?

Our projects explore a state-space perspective on biology. In this view, cells, organisms, ecosystems, and other complex systems are represented as points in a landscape defined by many interacting variables. The primary questions become geometric and dynamical rather than purely statistical. What is the shape of the space? Are there distinct regions, continuous gradients, or stable attractors? How do systems move through the landscape over time? What perturbations cause transitions between states, and what changes are required to guide a system from one region to another?

The goal is not simply to classify or predict, but to understand structure, dynamics, and control. By focusing first on the geometry of biological state spaces and only later on labels and categories, this approach seeks to uncover organizing principles that may be shared across many domains of biology. Ultimately, it is an attempt to develop a more intuitive and unified way of thinking about complex living systems.