Orthogonal dimensions

Using principles of orthogonality to describe and measure multidimensional uniqueness

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Nature does not live in databases. Nor is it neatly divisible. Certainly, our linear computing systems and statistics do poor justice to natural patterns like fractals. Indeed, many of our Indigenous friends bemoan the deconstructionist nature of industrial world analytics in the natural sciences (Forestiero 2022).

However, and pragmatically, the current economics of Nature are becoming increasingly computerized. Making databases or metrics that are overly simplified gives measurement noise, fails to account for harmful effects, and wastes time in confusion (Muller 2018). But its also true that simplifying data can lead to elegant solutions in complex systems that cannot be accurately characterized (Mitchell 2009). Additionally, multidimensional measurements can reduce harm by measuring unintended effects (Scott 1998).

Just like complex three-dimensional mathematical shapes can be described in an x-y-z axis, ecosystems can be better characterized in clean orthogonal dimensions. Orthogonality implies linear independence between dimensions (Szabo 2015), such that variation in one dimension (e.g., carbon) does not determine variation in another (e.g., biodiversity).

Orthogonal structures are essential for describing ecosystems such as forests exhibiting the ‘empty-forest syndrome’ (Redford 1992) or high-carbon monoculture agricultural systems where eucalyptus damages non-native water tables, or trees are planted in native grasslands (Villalba-Martínez et al. 2025). In all of these cases, carbon, biodiversity, and water show orthogonality (See Fig. B).

Figure B. World's shittiest graphic explaining the carbon and biodiversity markets

We think ecosystems are best characterized in six orthogonal dimensions, as defined in the Ecological Benefits Framework (EBF): soil, air, water, biodiversity, carbon, and equity. The framework was not developed through a top-down academic approach but through three sequential grassroots practitioner workgroups who collectively defined the dimensions based on their applied experience. The workgroups ran from peer expert networks recruited from ocean sustainable fishing, organic farming, and regenerative agriculture and converged reliably on the same dimensions.

Three of the EBF dimensions neatly align with the Rio Conventions, and have emerging or established markets with some standardization (see section The Protocol). Of these, only carbon has an easily agreed-upon unit, although the IBU biodiversity unit proposed later in this chapter does have market traction. The six dimensions each face independently emerging science and markets, and their interactions remain poorly characterized — a fragmentation that our stacking framework is specifically designed to navigate. But as a basic framework on which to orient, we think EBF is the most reliable place for anyone working with Nature from an industrial world context to start.