  We propose a method of classifying the operation of a system into finitely
many modes. Each mode has its own objectives for the system's behaviour and its
own mathematical models and algorithms designed to accomplish its objectives. A
central problem is deciding when to transition from one mode to some other
mode, a decision that may be contested and involve partial or inconsistent
information or evidence. We model formally the concept of modes for a system
and derive a family of data types for analysing mode transitions. The data
types are simplicial complexes, both abstract and realised in euclidean space
$\mathbb{R}^{n}$. In the data type, a mode is represented by a simplex. Each
state of a system can be evaluated relative to different modes by mapping it
into one or more simplices. This calibration measures the extent to which
distinct modes are appropriate for the state and can decide on a transition. We
explain this methodology based on modes, introduce the mathematical ideas about
simplicial objects we need and use them to build a theoretical framework for
modes and mode transitions. To illustrate the general model in some detail, we
work though a case study of an autonomous racing car.
