Variety distributions typically change continuously.
However, variety distributions can contain regions where they become discontinuous or exhibit cusp-like behaviours.
At these points, the variety landscape itself has a discontinuous structure, creating critical boundaries in the distributions of variety and power and control.
Discontinuities and cuspic changes in variety distributions mark points of irreversibility. These discontinuities in variety distributions can be either beneficial or problematic, depending on the context. Identifying where variety distributions have discontinuous boundaries is important for managing systems effectively.
Example: A man arranged for his donkey to be more cost-effective by training it to eat less and less until eventually it ate almost nothing – and died. The continuous reduction in food variety led to continuous changes in the donkey's viable-state variety distribution (thinner donkey, adjusted metabolism), but this variety distribution has a discontinuous boundary - at a critical threshold, the variety distribution suddenly excludes "living donkey" states. The food variety reduction was continuous; the variety distribution of viable donkey states became discontinuous at the death threshold. This discontinuity is irreversible.
Practical implications
It is important to:
- Identify if and where variety distributions have discontinuous boundaries
- Avoid unthinkingly crossing discontinuity boundaries or cuspic changes in variety distributions when managing real-world situations
- Observe, and if appropriate utilise, such discontinuities in adversarial systems' variety distributions (e.g., pushing weed variety distributions past viability boundaries)
- Monitor how variety distributions are changing to detect approach to discontinuous regions and the potential for disjoints in the locus and ownership in the distributions of power and control
Such discontinuities in variety distributions are sometimes called "tipping points" or irreversible boundaries.