Shape of Life

The Central Question

The goal is to move beyond descriptive morphology toward a mathematical
and physical account of form: a framework in which biological shapes can
be represented, compared, modeled, and simulated.

Vision

A morphodynamic atlas of life

We aim to reconstruct a quantitative map of how form changes across
development, ecology, and evolution. Within this atlas, shapes are treated
as points, paths, and distributions on high-dimensional geometric spaces.
Evolution becomes a flow through these spaces — constrained by physics,
shaped by development, and filtered by function and environment.

The project asks whether the diversity of living form can be understood
through a small number of interacting principles: geometry, growth,
physics, variation, constraint, and selection.

Why Now

A new synthesis is possible

Museum collections and digital scans provide unprecedented access to
fossil and extant forms. Discrete differential geometry allows complex
biological structures to be represented as analyzable meshes. Statistical
shape analysis and functional data methods make it possible to compare
forms across clades, environments, and developmental stages.

Physics links morphology to growth, elasticity, flow, fracture, and active
matter, while modern computation turns these ideas into generative and
testable models. Together, these tools make it possible to transform the
qualitative tree of life into a quantitative landscape of shape.

Scientific Goals

Represent and compare form

Develop robust geometric descriptions of biological shapes that preserve
curvature, topology, symmetry, scale, and connectivity — and statistical
and computational methods for comparing shapes across species, fossil
lineages, developmental stages, and ecological contexts.

Model form

Use physical and geometric principles to infer the rules by which forms
grow, deform, branch, fuse, fold, and fracture, and build generative
models capable of producing plausible morphologies consistent with
biological, developmental, and physical constraints.

Infer evolvability

Quantify how the capacity to generate new forms changes across
evolutionary history, ecological opportunity, and developmental
architecture.

Research Themes

Geometry of shape

Biological form treated through differential geometry, discrete geometry,
shape spaces, curvature flows, and diffeomorphic matching.

Physics of morphogenesis

Growth, rheology, active stresses, and material constraints modeled as
drivers of form.

Statistical morphology

Shape variation analyzed using statistical inference, functional data
analysis, information geometry, and probabilistic models.

Evolutionary dynamics

Fossil and extant morphologies interpreted as samples from evolving
distributions of form, constrained by phylogeny, development, and
environment.

Computation and simulation

Geometry-aware algorithms, differentiable solvers, and machine learning
tools connecting raw scans to models, inference, and prediction.

The Collaboratory

Form as both data and dynamics

Shape of Life is designed as a collaboratory linking mathematicians,
physicists, computer scientists, statisticians, biologists,
paleontologists, and museum collections. No single field can solve the
problem of form. Geometry provides representation. Physics provides
mechanism. Statistics provides inference. Computation provides scale.
Biology and paleontology provide meaning, constraint, and reality.

People

Group members