homology

To find all the types of holes within a particular topological shape, mathematicians build something called a chain complex, which forms the scaffolding of homology.

So instead, homology infers an object’s holes from its boundaries, a more precise mathematical concept.

Mathematicians extract a shape’s homology from its chain complex, which provides structured data about the shape’s component parts and their boundaries — exactly what you need to describe holes in every dimension.

The idea was to take the idea of homology—similarity due to shared evolutionary history—and build a predictive model of plant variation.

The modern definition of homology is quite involved, but it is roughly a means of associating to each shape a certain mathematical object.

Homology is still determined by position, by connections, in the embryo as in the adult.